ramification index

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• ramification — index organ Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

• Ramification — 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… …   Wikipedia

• Ramification theory of valuations — In mathematics, the ramification theory of valuations studies the set of extensions of a valuation v of a field K to an extension L of K. It is a generalization of the ramification theory of Dedekind domains. Contents 1 Galois case 1.1… …   Wikipedia

• Splitting of prime ideals in Galois extensions — In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one of the richest parts of… …   Wikipedia

• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• Riemann-Hurwitz formula — In mathematics, the Riemann Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. It therefore connects ramification… …   Wikipedia

• Valuation (algebra) — In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… …   Wikipedia

• Different ideal — In algebraic number theory, the different ideal (sometimes simply the different) is defined to account for the (possible) lack of duality in the ring of integers of an algebraic number field K, with respect to the field trace. It was introduced… …   Wikipedia

• Hurwitz's theorem — In mathematics, Hurwitz s theorem is any of at least five different results named after Adolf Hurwitz. Hurwitz s theorem in complex analysis In complex analysis, Hurwitz s theorem roughly states that, under certain conditions, if a sequence of… …   Wikipedia

• Decomposition des ideaux premiers dans les extensions galoisiennes — Décomposition des idéaux premiers dans les extensions galoisiennes En mathématiques, l interaction entre le groupe de Galois d une extension galoisienne de corps de nombres (ou de corps de nombres p adiques, ou de corps de fonctions), et la… …   Wikipédia en Français

• Décomposition Des Idéaux Premiers Dans Les Extensions Galoisiennes — En mathématiques, l interaction entre le groupe de Galois d une extension galoisienne de corps de nombres (ou de corps de nombres p adiques, ou de corps de fonctions), et la manière dont les idéaux premiers de l anneau des entiers algébriques …   Wikipédia en Français