- indecomposable module
- мат.неразложимый модуль
English-Russian scientific dictionary. 2008.
indecomposable module
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Indecomposable module — In abstract algebra, a module is indecomposable if it is non zero and cannot be written as a direct sum of two non zero submodules.Indecomposable is a weaker notion than simple module:simple means no proper submodule N < M,while indecomposable… … Wikipedia
Indecomposable — has multiple meanings in the field of mathematics:* indecomposable module, in algebra * indecomposable distribution, in probability * indecomposable continuum, in topology * indecomposability, in constructive mathematics … 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
Module Simple — Un module M sur un anneau A est dit simple ou irréductible si et seulement si M n est pas le module nul et il n existe pas de sous modules de M en dehors de {0} et M. Exemples Un espace vectoriel de dimension 1 est un module simple. Étant donné… … Wikipédia en Français
Module simple — Un module M sur un anneau A est dit simple ou irréductible si M n est pas le module nul et il n existe pas de sous modules de M en dehors de {0} et M. Sommaire 1 Exemples 2 Structure des modules simples 3 Propriétés … Wikipédia en Français
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
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
Algebraically compact module — In mathematics, especially in the area of abstract algebra known as module theory, algebraically compact modules, also called pure injective modules, are modules that have a certain nice property which allows the solution of infinite systems of… … 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
Semisimple module — In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over… … Wikipedia
Modular representation theory — is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic. As well as having applications to group theory, modular representations arise… … Wikipedia
