- ramification theory
- мат.теория ветвления
English-Russian scientific dictionary. 2008.
ramification theory
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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
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 problem — In philosophy and AI (especially, knowledge based systems), the ramification problem is concerned with indirect consequences of an action. It might be posed as how to represent what happens implicitly due to an action or to control secondary and… … Wikipedia
Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. Contents 1 Local… … Wikipedia
Conway notation (knot theory) — Left: A tangle a and its reflection a. Top right: Tangle addition, denoted by a + b. Center right: Tangle product, denoted by a b, equivalent to a + b. Bottom right: Ramification, denoted by a , b, equivalent to a + b In knot theory, Conway… … Wikipedia
List of algebraic number theory topics — This is a list of algebraic number theory topics. Contents 1 Basic topics 2 Important problems 3 General aspects 4 Class field theory … Wikipedia
Modulus (algebraic number theory) — In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle,[1] or extended ideal[2]) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to… … Wikipedia
Galois module — In mathematics, a Galois module is a G module where G is the Galois group of some extension of fields. The term Galois representation is frequently used when the G module is a vector space over a field or a free module over a ring, but can also… … 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
Newton polygon — In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields. In the original case, the local field of interest was the field of formal Laurent series in the indeterminate X, i.e. the field of… … Wikipedia
Tensor product of fields — In abstract algebra, the theory of fields lacks a direct product: the direct product of two fields, considered as a ring is never itself a field. On the other hand it is often required to join two fields K and L, either in cases where K and L are … Wikipedia
