finitely generated ring
1Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… …
2Finitely generated module — In mathematics, a finitely generated module is a module that has a finite generating set. Equivalently, it is a homomorphic image of a free module on finitely many generators. The kernel of this homomorphism need not be finitely generated (then… …
3Finitely generated algebra — In mathematics, a finitely generated algebra is an associative algebra A over a field K such that every element of A can be expressed as a polynomial in a finite set of elements a 1, hellip;, a n of A , with coefficients in K . If it is necessary …
4Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… …
5Ring (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… …
6Glossary 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… …
7Noetherian ring — In mathematics, more specifically in the area of modern algebra known as ring theory, a Noetherian ring, named after Emmy Noether, is a ring in which every non empty set of ideals has a maximal element. Equivalently, a ring is Noetherian if it… …
8Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with …
9Von Neumann regular ring — In mathematics, a ring R is von Neumann regular if for every a in R there exists an x in R with : a = axa .One may think of x as a weak inverse of a ; note however that in general x is not uniquely determined by a .(The regular local rings of… …
10Nagata ring — In commutative algebra, an integral domain A is called an N 1 ring if its integral closure in its quotient field is a finitely generated A module. It is called a Japanese ring (or an N 2 ring) if for every finite extension L of its quotient field …
