ring isomorphism
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Isomorphism (disambiguation) — Isomorphism may refer to:* Isomorphism, in mathematics, a mapping that preserves the structure * Group isomorphism, in mathematics, a mapping that preserves the group structure * Ring isomorphism, in mathematics, a mapping that preserves both the … 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
Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia
Ring homomorphism — In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication. More precisely, if R and S are rings, then a ring homomorphism is a function f : R → S such that … Wikipedia
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
Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… … Wikipedia
Isomorphism of categories — In category theory, two categories C and D are isomorphic if there exist functors F : C rarr; D and G : D rarr; C which are mutually inverse to each other, i.e. FG = 1 D (the identity functor on D ) and GF = 1 C . This means that both the objects … Wikipedia
Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… … Wikipedia
Quotient ring — In mathematics a quotient ring, also known as factor ring or residue class ring, is a construction in ring theory, quite similar to the factor groups of group theory and the quotient spaces of linear algebra. One starts with a ring R and a two… … Wikipedia
Matrix ring — In abstract algebra, a matrix ring is any collection of matrices forming a ring under matrix addition and matrix multiplication. The set of n×n matrices with entries from another ring is a matrix ring, as well as some subsets of infinite matrices … Wikipedia
Burnside ring — In mathematics, the Burnside ring of a finite group is an algebraic construction that encodes the different ways the group can act on finite sets. The ideas were introduced by William Burnside at the end of the nineteenth Century, but the… … Wikipedia
