- cyclic submodule
- мат. циклический подмодуль
Большой англо-русский и русско-английский словарь. 2001.
cyclic submodule
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Cyclic module — In mathematics, more specifically in ring theory, a cyclic module is a module over a ring which is generated by one element. The term is by analogy with cyclic groups, that is groups which are generated by one element. Contents 1 Definition 2… … Wikipedia
Torsion (algebra) — In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Definition Let G be a group. An element g of G is called a torsion element if g has… … Wikipedia
Structure 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… … Wikipedia
Module (mathematics) — For other uses, see Module (disambiguation). In abstract algebra, the concept of a module over a ring is a generalization of the notion of vector space, wherein the corresponding scalars are allowed to lie in an arbitrary ring. Modules also… … Wikipedia
Injective module — In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z module Q of all rational numbers. Specifically, if Q is a submodule of some… … Wikipedia
Simple module — In abstract algebra, a (left or right) module S over a ring R is called simple or irreducible if it is not the zero module 0 and if its only submodules are 0 and S . Understanding the simple modules over a ring is usually helpful because these… … Wikipedia
Finitely-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… … Wikipedia
Serial module — Chain ring redirects here. For the bicycle part, see Chainring. In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any two submodules N1 and N2 of M,… … Wikipedia
Artinian module — In abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its submodules. They are for modules what Artinian rings are for rings, and a ring is Artinian if and only if it is an Artinian module over… … Wikipedia
Dedekind domain — In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily … Wikipedia
Length of a module — In abstract algebra, the length of a module is a measure of the module s size . It is defined as the length of the longest ascending chain of submodules and is a generalization of the concept of dimension for vector spaces. The modules with… … Wikipedia
