- algebra module
- мат.модуль над алгеброй
English-Russian scientific dictionary. 2008.
algebra module
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Algebra (ring theory) — In mathematics, specifically in ring theory, an algebra over a commutative ring is a generalization of the concept of an algebra over a field, where the base field K is replaced by a commutative ring R .Any ring can be thought of as an algebra… … 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 plat — La notion de module plat a été introduite par Jean Pierre Serre[1]. Elle généralise les modules projectifs et a fortiori les modules libres. En algèbre commutative et en géométrie algébrique, cette notion a été notamment exploitée par Alexander… … Wikipédia en Français
Algebra representation — In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint… … Wikipedia
Algebra over a field — This article is about a particular kind of vector space. For other uses of the term algebra , see algebra (disambiguation). In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it is… … Wikipedia
Module artinien — En théorie des anneaux, un module artinien (du nom d Emil Artin) est un module vérifiant la condition des chaines décroissantes. C est une sorte de généralisation des espaces vectoriels de dimension finie. Sommaire 1 Définition 2 Exemples 3… … Wikipédia en Français
Module — A module is a self contained component of a system, which has a well defined interface to the other components; something is modular if it includes or uses modules which can be interchanged as units without disassembly of the module. Design,… … Wikipedia
Projective module — In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). Various equivalent… … Wikipedia
Fundamental theorem of algebra — In mathematics, the fundamental theorem of algebra states that every non constant single variable polynomial with complex coefficients has at least one complex root. Equivalently, the field of complex numbers is algebraically closed.Sometimes,… … Wikipedia
Von Neumann algebra — In mathematics, a von Neumann algebra or W* algebra is a * algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann,… … Wikipedia
List of abstract algebra topics — Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this … Wikipedia
