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isomorphism theorem

См. также в других словарях:

  • Isomorphism theorem — In mathematics, specifically abstract algebra, the isomorphism theorems are three theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules,… …   Wikipedia

  • Norm residue isomorphism theorem — In the mathematical field of algebraic K theory, the norm residue isomorphism theorem is a long sought result whose complete proof was announced in 2009. It previously was known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato,… …   Wikipedia

  • Myhill isomorphism theorem — For the Goodman–Myhill theorem in constructive set theory, see Diaconescu s theorem. In computability theory the Myhill isomorphism theorem, named after John Myhill, provides a characterization for two numberings to induce the same notion of… …   Wikipedia

  • Isomorphism extension theorem — In field theory, a branch of mathematics, the isomorphism extension theorem is an important theorem regarding the extension of a field isomorphism to a larger field. Isomorphism extension theorem The theorem states that given any field F, an… …   Wikipedia

  • Isomorphism — In abstract algebra, an isomorphism (Greek: ἴσος isos equal , and μορφή morphe shape ) is a bijective map f such that both f and its inverse f −1 are homomorphisms, i.e., structure preserving mappings.In the more general setting of category… …   Wikipedia

  • Graph isomorphism — In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if ƒ(u) and ƒ(v) are adjacent in H. This kind of bijection is commonly… …   Wikipedia

  • Cayley's theorem — In group theory, Cayley s theorem, named in honor of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group on G . This can be understood as an example of the group action of G on the elements of G .A… …   Wikipedia

  • Rank–nullity theorem — In mathematics, the rank–nullity theorem of linear algebra, in its simplest form, states that the rank and the nullity of a matrix add up to the number of columns of the matrix. Specifically, if A is an m by n matrix over the field F , then :rank …   Wikipedia

  • Fundamental theorem on homomorphisms — In abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism.The… …   Wikipedia

  • Lattice theorem — In mathematics, the lattice theorem, sometimes referred to as the fourth isomorphism theorem or the correspondence theorem, states that if N is a normal subgroup of a group G, then there exists a bijection from the set of all subgroups A of G… …   Wikipedia

  • Chinese remainder theorem — The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. In its most basic form it concerned with determining n, given the remainders generated by division of n by several numbers.… …   Wikipedia

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