Ramification

Definitions: Ramification

Ramification

Noun

1. The act of branching out or dividing into branches.

2. A development that complicates a situation; "the court's decision had many unforeseen ramifications".

Date "ramification" was first used in popular English literature: sometime before 1843. (references)

Etymology: Ramification \Ram`i*fi*ca"tion\, noun. [Compare to the French expression ramification. See Ramify.]. (Websters 1913)

Domain	Definitions
Medicine	The act or process of branching; a small branch from a main nerve or blood vessel. Source: European Union. (references)
Source: compiled by the editor from various references; see credits.

In mathematics, ramification is a geometric term used for 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. It is also used from the opposite perspective (branches coming together) as when a covering map degenerates at a point of a space, with some collapsing together of the fibers of the mapping.

The basic model can be taken as the z -> zⁿ mapping in the complex plane, near z = 0. This is the standard local picture in Riemann surface theory, of ramification of order n. It occurs for example in the Riemann-Hurwitz formula for the effect of mappings on the genus.

In a covering map the Euler-Poincaré characteristic should multiply by the number of sheets; ramification can therefore be detected by some dropping from that. The z -> zⁿ mapping shows this as a local pattern: if we exclude 0, looking at 0 < |z| < 1 say, we have (from the homotopy point of view) the circle mapped to itself by the n-th power map (Euler-Poincaré characteristic 0), but with the whole disk the Euler-Poincaré characteristic is 1, n-1 being the 'lost' points as the n sheets come together at z = 0.

In geometric terms, ramification is something that happens in codimension two (like knot theory, and monodromy); since real codimension two is complex codimension one, the local complex example sets the pattern for higher-dimensional complex manifolds. In complex analysis, sheets can't simply fold over along a line (one variable), or codimension one subspace in the general case. The ramification set (branch locus on the base, double point set above) will be two dimensions lower than the ambient manifold, and so will not separate it into two 'sides', locally - there will be paths that trace round the branch locus, just as in the example. In algebraic geometry over any field, by analogy, it also happens in algebraic codimension one.

Ramification in algebraic number theory means prime numbers factorising into some repeated prime ideal factors. If R is the ring of integers of an algebraic number field K and P a prime ideal of R. for each extension field L of K we can consider the integral closure S of R in L and the ideal PS of S. This may or may not be prime, but assuming [L:K] is finite it is a product of prime ideals P₁^e(1)...P_k^e(k) where the P_i are distinct prime ideals of S. Then P is said to ramify in L if some e(i) > 1. An equivalent condition is that S/PS has a non-zero nilpotent element - is not a product of finite fields. The analogy with the Riemann surface case was already pointed out by Dedekind and Weber in the nineteenth century. The ramification is tame when the e(i) are all less than the residue characteristic p of P. This condition is important in Galois module theory.

Synonyms: Ramification

Synonyms: branching (n), complication (n), fork (n), forking (n). (additional references)

Context	Synonyms within Context (source: adapted from Roget's Thesaurus).
bisection	Bifurcation, forking, branching, ramification, divarication; fork, prong; fold. half, moiety.
Divergence	Noun: divergence, divergency; divarication, ramification, forking; radiation; separation; (disjunction); dispersion; deviation; aberration.
Filament	Beard; (roughness); ramification; strand.
Part	Debris, odds and ends, oddments, detritus; excerpta; member, limb, lobe, lobule, arm, wing, scion, branch, bough, joint, link, offshoot, ramification, twig, bush, spray, sprig; runner; leaf, leaflet; stump; component part; sarmentum.
Posterity	Child, son, daughter; butcha; bantling, scion; acrospire, plumule, shoot, sprout, olive-branch, sprit, branch; off-shoot, off-set; ramification; descendant; heir, heiress; heir-apparent, heir-presumptive; chip off the old block; heredity; rising generation.
Symmetry	Arborescence, branching, ramification; arbor vitae.
Source: adapted from Roget's Thesaurus.

Crosswords: Ramification

Non-English Usage: "Ramification" is also a word in the following language with English translations in parentheses.

French (branch, corrugation, fork, offshoot, ramification).

"Ramification" is generally used as a noun (singular) -- approximately 100.00% of the time. "Ramification" is used about 2 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)

Parts of Speech	Percent	Usage per 100 Million Words	Rank in English
Noun (singular)	100%	2	245,945

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.

Language		Translations for "ramification"; alternative meanings/domain in parentheses.
Albanian		zgjerim (amplification, dilatation, dilation, distention, diversification, enlargement, expanse, expansion, extension, spreading, widening), shtrirje (compass, dimension, elongation, expansion, extension, extent, lie, make believe, prolongation, proportions, rame, range, reach, scope, spread, spreading, stretch, swing), degëzim (arm, bifurcation, branch, derivation, embranchment, feeder, fork, furcation, prong, rame, spur), degë druri, degë (agency, arm, bough, branch, brushwood, department, discipline, embranchment, fork, knag, limb, offshoot, outgrowth, perch, prong, rame, specialism, stick). (various references)

Arabic		‏فروع شركة, ‏فرع شعبة (branch, division, fork, section), ‏نتيجة (conclusion, consequence, echo, effect, emanation, end, event, fruit, offshoot, offspring, outcome, payoff, precipitate, product, progeny, purpose, repercussion, result, score, sequel, termination, upshot, work), ‏تغصن (offshoot, ruckle), ‏تشعب (bisect, branch, calve, diverge, divergence, fork, offshoot, radiate, ramify, split, split up), ‏عاقبة (consequence, sequel, wage), ‏شعبة (branch, department, division, section), ‏شعب علم. (various references)

Bulgarian		усложнение (complication, difficulty, embroilment, involvement, knot), разклонение (branch, derivation, embranchment, node, offset, offshoot, prong, ramus, split, tap), отклонение (aberration, bias, declination, deflection, deflexion, derivation, detour, deviation, digression, divergence, divergency, diversion, drift, excursion, inflection, inflexion, lapse, shunt, swerve, turnout, variation), последица (after effect, backwash, consequence, effect, follow up, issue, offspring, outgrowth, progeny, repercussion, result, sequel, train, upshot), подразделение (partition, section, subdivision, subspecies), поделение (detachment, division, element, outfit, section, unit). (various references)

Chinese		分枝 (Bifurcated, Outgrowth). (various references)

Czech		rozvìtvení (embranchment), rodokmen (family tree, lineage, pedigree), dùsledek (consequence, corollary, implication, inference, result, sequel). (various references)

Danish		ramifikation (branching), forgrening (branch, branching, bypass, junction, leg, side chain, side road, signing intersection). (various references)

Dutch		ramificatio (branching), ramificatie (branching), vertakking (branching, demerge, diverge, junction, lineage, roadway junction). (various references)

Farsi		انشعاب (Divergence, Junction, Offshoot, Shoot, Tributary), شاخه شاخگی . (various references)

Finnish		haarautuminen (branching, lineage). (various references)

French		ramification. (various references)

German		Verzweigung (branch, branching, fork, lineage), Verästelung (branching). (various references)

Greek		διακλάδωση (a fork, arm, bifurcation, branch, branch line, branching, electric shunt, fork, junction, parallel resistance, points, points switch, prong, shunt, shunting, spur, switch point, turnout). (various references)

Hebrew		�"סתעפות (branching off, divergence). (various references)

Hungarian		elágazás (arm, bifurcation, branch, branching, crotch, derivation, divergence, divergency, fork, intersection, junction, offset, turnout), elágasodás, ágazat (arm, branch, loft, major, sector, shroud, specialization). (various references)

Italian		ramificazione (antler, branching), diramazione (bifurcation, branch, branch line, branch line carrying feeder, demerge, diverge, feeder line, fork, issuing, junction, peripheral, sending out, side road, signing intersection, switch point, traffic). (various references)

Japanese Kanji		枝分かれ (branch). (various references)

Japanese Katakana		え� わかれ (branch). (various references)

Korean		파생효과. (various references)

Manx		stholey (branch, branching, ramify, shoot of plant, sprout, stool). (various references)

Pig Latin		amificationray.(various references)

Portuguese		ramificação (arm, branch, branching, embrangle, offshoot, ramus, sub-lateral). (various references)

Romanian		ramificare (embranchment, offset, parting), ramificaţie (bend, branch, offshoot, split, spur, tap). (various references)

Russian		разветвление (bifurcation, divarication, embranchment, furcation, parting). (various references)

Serbo-Croatian		razgranjavanje, razgranatost. (various references)

Spanish		ramificación (branch, branching). (various references)

Swedish		förgrening (branch, branching, demerge, diverge, fork, side chain). (various references)

Thai		การแตกสาขา. (various references)

Turkish		kollara ayrılma, kol (arm, branch, crank, embranchment, flipper, foreleg, handle, limb, offset, rod, rounds, sleeve, stick, stolon, subsection, tappet, wing), dallanma (branching, embranchment, furcation), dallanıp budaklanma, dal (arm, bough, branch, offset, offshoot, subsection, twig), şube (arm, branch, branch office, department, limb, offshoot, substation). (various references)

Ukranian		розгалуження, результат (conclusion, consequence, consequent, corollary, development, eduction, effect, end, issue, offspring, omnium, outcome, outgrowth, output, produce, product, progeny, purpose, result, subsequence, termination, upshot), паросток (appendage, bine, browse, offset, offspring, outgrowth, process, provine, slip, sprout). (various references)

Vietnamese		sự phân nhánh (embranchment), sự chia nhánh nhánh, chi nhánh. (various references)
Source: compiled by the editor from various translation references.

Language	Period	Translations
Latin	500 BCE-Modern	ramificatio. (various references)
Source: compiled by the editor from various references.

Derivations
	Words beginning with "ramification": ramifications. (additional references)
Misspellings
	"Ramification" is suggested in spellcheckers for the following: eradification, irradification, ramafication, ramfication, ramnification, remification. (additional references)
Source: compiled by the editor, based on several corpora (additional references).

# of Phoneme Matches	Pronunciation	Word(s) rhyming with "ramification" (pronounced ra'mufukā"shun)
8	-u f u k ā" sh u n	acidification, amplification, certification, classification, codification, decertification, deification, disqualification, diversification, edification, falsification, fortification, gasification, gratification, identification, intensification, magnification, modification, notification, nullification, ossification, pacification, personification, purification, qualification, quantification, ratification, recertification, reclassification, rectification, reunification, sanctification, saponification, unification, verification, vilification.
7	-f u k ā" sh u n	pontification, suffocation.
6	-u k ā" sh u n	adjudication, advocation, allocation, application, authentication, avocation, communication, complication, convocation, dedication, desiccation, domestication, duplication, education, equivocation, eradication, excommunication, explication, implication, indication, intoxication, invocation, medication, misallocation, misapplication, miscommunication, multiplication, prefabrication, prognostication, provocation, reallocation, rededication, replication, revocation, vindication.
5	-k ā" sh u n	abdication, altercation, bifurcation, clarification, confiscation, demarcation, detoxication, detoxification, disembarkation, dislocation, echolocation, electrification, embarkation, evocation, fabrication, gentrification, glorification, indemnification, justification, location, lubrication, misidentification, mummification, obfuscation, publication, relocation, simplification, sophistication, specification, syndication, telecommunication, vacation, vocation.
4	-ā" sh u n	abbreviation, aberration, abomination, abrogation, acceleration, acclimation, accommodation, accreditation, accumulation, accusation, activation, adaptation, administration, admiration, adoration, adulation, affectation, affiliation, affirmation, agglomeration, aggravation, agitation, alienation, allegation, alleviation, alphabetization, alteration, amalgamation, amelioration, amortization, amputation, animation, annexation, annihilation, annotation, anticipation, antidiscrimination, appellation, appreciation, approbation, appropriation, approximation, arbitration, argumentation, articulation, aspiration, assassination, assimilation, association, augmentation, authorization, automation, aviation, balkanization, calculation, calibration, cancellation, cannibalization, capitalization, capitulation, carnation, castration, categorization, causation, celebration, centralization, cessation, cetacean, characterization, citation, civilization, coagulation, cogeneration, cogitation, cohabitation, collaboration, collectivization, colonization, coloration, colorization, combination, commemoration, commendation, commercialization, communization, compensation, compilation, computation, computerization, concatenation, concentration, conciliation, condemnation, condensation, confabulation, confederation, configuration, confirmation, conflagration, confrontation, conglomeration, congratulation, congregation, conjugation, connotation, consecration, conservation, consideration, consolation, consolidation, constellation, consternation, constipation, consultation, consummation, contamination, contemplation, continuation, conversation, cooperation, coordination, coronation, corporation, correlation, corroboration, creation, cremation, criminalization, crustacean, culmination, cultivation, dalmatian, damnation, decaffeination, decapitation, deceleration, decentralization, declaration, decontamination, decoration, decriminalization, defamation, deflation, deforestation, deformation, degeneration, degradation, dehumanization, dehydration, deinstitutionalization, delegation, deliberation, delineation, demilitarization, demobilization, democratization, demodulation, demonization, demonstration, demoralization, denationalization, denomination, denuclearization, denunciation, depopulation, deportation, depravation, depreciation, depredation, deprivation, deregulation, derivation, desalination, desalinization, desecration, desegregation, designation, desolation, desperation, destabilization, destination, determination, detonation, devaluation, devastation, deviation, dictation, differentiation, dilatation, dilation, discoloration, discontinuation, discrimination, disinclination, disinflation, disinformation, disintegration, disorganization, disorientation, dispensation, disputation, dissemination, dissertation, dissipation, dissociation, distillation, divination, documentation, domination, donation, dramatization, duration, ejaculation, elaboration, elation, elevation, elimination, elongation, emanation, emancipation, emigration, emulation, enumeration, equalization, equitation, escalation, estimation, evacuation, evaluation, evaporation, exacerbation, exaggeration, examination, exasperation, excavation, excitation, exclamation, exfoliation, exhalation, exhilaration, exhortation, exhumation, exoneration, expatriation, expectation, experimentation, expiration, explanation, exploitation, exploration, expropriation, extermination, extrapolation, facilitation, fascination, federation, fermentation, fertilization, fibrillation, figuration, filtration, fixation, flirtation, flotation, fluctuation, fluoridation, foliation, formation, formulation, foundation, fragmentation, frustration, fumigation, gastrulation, generalization, generation, germination, gestation, glaciation, globalization, gradation, graduation, granulation, gravitation, gyration, habitation, hallucination, harmonization, hesitation, hibernation, hospitalization, humiliation, hybridization, hydration, hydrogenation, hyperinflation, illumination, illustration, imagination, imitation, immigration, immunization, impersonation, implantation, implementation, importation, impregnation, improvisation, imputation, inactivation, inauguration, incantation, incapacitation, incarceration, incarnation, inclination, incoordination, incorporation, incrimination, incrustation, incubation, indentation, indexation, indignation, indoctrination, industrialization, infatuation, infestation, infiltration, inflammation, inflation, information, inhabitation, inhalation, initiation, innovation, inoculation, insemination, insinuation, inspiration, installation, instigation, institutionalization, instrumentation, insubordination, insulation, integration, internationalization, interpretation, interrogation, intimation, intimidation, intonation, inundation, invalidation, investigation, invitation, ionization, irradiation, irrigation, irritation, isolation, jubilation, laceration, lactation, legalization, legislation, levitation, liberalization, liberation, libration, ligation, limitation, liquidation, litigation, localization, machination, magnetization, malformation, manifestation, manipulation, marginalization, masturbation, maturation, maximization, mechanization, mediation, meditation, menstruation, migration, mineralization, miniaturization, ministration, misappropriation, miscalculation, mischaracterization, miscreation, misinformation, misinterpretation, misrepresentation, mitigation, mobilization, moderation, modernization, modulation, molestation, monopolization, motivation, mutation, mutilation, narration, nation, nationalization, naturalization, navigation, negation, negotiation, neutralization, nitration, nomination, nondiscrimination, nonproliferation, normalization, notation, nucleation, obligation, observation, occupation, operation, optimization, oration, orchestration, ordination, organisation, organization, orientation, origination, ornamentation, oscillation, ostentation, ovation, overpopulation, overregulation, overvaluation, ovulation, oxidation, pagination, palpitation, participation, pasteurization, penetration, perforation, permutation, perpetuation, personalization, perspiration, perturbation, pigmentation, plantation, polarization, politicization, pollination, popularization, population, precipitation, predestination, premeditation, preoccupation, preparation, presentation, preservation, pressurization, privation, privatization, probation, proclamation, procrastination, procreation, profanation, proliferation, pronunciation, propagation, proration, prostration, protestation, punctuation, quotation, radiation, radicalization, rationalization, reaffirmation, realization, reauthorization, recalculation, recantation, recapitalization, recitation, reclamation, recommendation, reconciliation, reconfiguration, reconfirmation, reconsideration, recreation, recrimination, recuperation, redecoration, reevaluation, reexamination, reflation, reforestation, reformation, refrigeration, refutation, regeneration, regimentation, registration, regulation, rehabilitation, rehydration, reincarnation, reincorporation, reinterpretation, reinvigoration, reiteration, rejuvenation, relation, relaxation, remediation, remuneration, renationalization, renegotiation, renomination, renovation, renunciation, reorganization, reparation, repatriation, representation, repudiation, reputation, reregulation, reservation, resignation, respiration, restoration, resuscitation, retaliation, retardation, revaluation, revelation, reverberation, revitalization, rotation, rumination, salvation, sanitation, saturation, securitization, sedation, sedimentation, segmentation, segregation, sensation, separation, sequestration, simulation, situation, socialization, solicitation, specialization, speculation, stabilization, stagflation, stagnation, standardization, starvation, station, sterilization, stimulation, stipulation, strangulation, subluxation, subordination, subsidization, substantiation, suburbanization, summation, superstation, tabulation, taxation, temptation, termination, titillation, toleration, transformation, transillumination, translation, transplantation, transportation, trepidation, triangulation, tribulation, undervaluation, unionization, urbanization, usurpation, utilization, vaccination, vacillation, validation, valuation, vaporization, variation, vegetation, ventilation, vibration, victimization, violation, visitation, visualization, vulgarization, westernization.
3	-sh u n	abduction, abolition, abortion, absolution, absorption, abstraction, academician, accession, accretion, acquisition, action, addiction, addition, admission, admonition, adoption, advection, affection, affliction, aggression, alliteration, alternation, ambition, ammunition, antiabortion, anticorruption, apparition, apportion, apprehension, ascension, ashen, assertion, assumption, attention, attraction, attribution, attrition, auction, audition, beautician, benediction, brutalization, caption, carburetion, caution, circulation, circumspection, clinician, coalition, coercion, cognition, collection, commission, commotion, compassion, competition, completion, complexion, composition, comprehension, compression, compulsion, compunction, conception, conceptualization, concession, concoction, concussion, condescension, condition, conduction, confection, confession, conjunction, connection, conniption, conscription, constitution, constriction, construction, consumption, contention, contortion, contraception, contraction, contradiction, contraption, contribution, contrition, convection, convention, conviction, convolution, convulsion, correction, corruption, counterrevolution, crucifixion, cushion, deception, decimation, decommission, decomposition, decompression, deconstruction, deduction, defection, definition, deletion, demolition, demotion, dentition, depiction, depletion, deposition, depression, dereliction, description, desertion, destitution, destruction, detection, detention, deterioration, devolution, devotion, diction, dietitian, diffraction, digression, dilution, dimension, diminution, direction, disaffection, disconnection, discretion, discussion, disinfection, disposition, disruption, dissatisfaction, dissection, dissension, dissolution, distinction, distortion, distraction, distribution, dysfunction, edition, egyptian, ejection, election, electrician, electrocution, elocution, emission, emotion, emulsion, encryption, erection, erudition, eruption, eviction, evolution, exaction, exception, excoriation, excretion, execution, exemption, exertion, exhibition, expansion, expedition, exposition, expression, expulsion, extension, extinction, extortion, extraction, extradition, faction, fashion, fiction, fission, flexion, formalization, fraction, freshen, friction, fruition, function, gentian, geriatrician, gumption, hessian, homogenization, hypertension, hypotension, ignition, impassion, imperfection, imposition, impression, inaction, inception, incineration, indiscretion, induction, infarction, infection, inflection, infliction, infraction, inhibition, injection, injunction, inquisition, inscription, insertion, inspection, institution, instruction, insurrection, interaction, interception, intercession, interconnection, interdiction, interjection, intermission, interruption, intersection, introduction, introspection, intuition, invention, junction, jurisdiction, juxtaposition, lilliputian, liposuction, liquefaction, locomotion, logician, lotion, magician, malfunction, malnutrition, mansion, martian, mathematician, mention, midsection, misapprehension, misconception, misimpression, misperception, mission, mortician, motion, munition, musician, nonaggression, nonfiction, nonprescription, notion, nutrition, objection, obsession, obstetrician, obstruction, ocean, omission, opposition, oppression, optician, option, overconsumption, overexpansion, overproduction, overprotection, overreaction, oversimplification, partition, passion, patrician, pediatrician, pension, perception, percussion, perfection, permission, persecution, petition, physician, politician, pollution, portion, position, possession, potion, precaution, precession, preconception, precondition, prediction, predilection, predisposition, preelection, preemption, preignition, premonition, prescription, presumption, presupposition, pretension, prevention, procession, production, profession, progression, prohibition, projection, promotion, proportion, proposition, propulsion, proscription, prosecution, prostitution, protection, ration, reaction, reassertion, reception, recession, recognition, recollection, recondition, reconstruction, redefinition, redemption, redirection, redistribution, reduction, reeducation, reelection, reflection, regression, reimposition, reinspection, reintegration, reintroduction, reinvention, rejection, remission, rendition, repercussion, repetition, reposition, repossession, repression, reproduction, requisition, resolution, restitution, restriction, resumption, resurrection, retention, retraction, retransmission, retribution, revolution, revulsion, rhetorician, sanction, satisfaction, secession, secretion, section, sedition, seduction, selection, session, solution, statistician, submission, subscription, subsection, substation, substitution, subtraction, succession, suction, superstition, supposition, suppression, suspension, suspicion, syncopation, tactician, technician, tension, theoretician, titian, traction, tradition, transaction, transcription, transection, transgression, transition, transmission, tuition, venetian, volition, workstation.
Source: compiled by the editor (additional references); see credits.

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "a-a-c-f-i-i-i-m-n-o-r-t"
	-3 letters: mortician.
	-4 letters: amniotic, anatomic, animator, antifoam, armonica, aromatic, foramina, fraction, friction, macaroni, marocain, morainic, raincoat, romantic.
	-5 letters: aciform, acromia, actinia, amorini, animato, antiair, anticar, carotin, comitia, confirm, faction, fanatic, fiction, formant, frantic, infarct, infract, manioca, mantric, marcato, martian, martini, minicar, minorca, motific, noritic, ocarina, omnific, tamarin.
	Words containing the letters "a-a-c-f-i-i-i-m-n-o-r-t"
	+1 letter: ramifications.
Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.