- bimodule
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An abelian group that is both a left and a right module, such that the left and right multiplications are compatible
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bimodule
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Bimodule — In abstract algebra a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in … Wikipedia
Bimodule — Un A1 A2 bimodule est un ensemble M muni à la fois d une structure de module à gauche sur un anneau A1 et d une structure de module à droite sur un anneau A2 vérifiant . Exemples Tout A module à droite est aussi un A bimodule A es … Wikipédia en Français
Tensor product of modules — In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (roughly speaking, multiplication ) to be carried out in terms of linear maps (module homomorphisms). The module construction is analogous… … Wikipedia
Noetherian module — In abstract algebra, an Noetherian module is a module that satisfies the ascending chain condition on its submodules, where the submodules are partially ordered by inclusion. Historically, Hilbert was the first mathematician to work with the… … Wikipedia
Subfactor — In the theory of von Neumann algebras, a subfactor of a factor M is a subalgebra that is a factor and contains 1. The theory of subfactors led to the discovery of the Jones polynomial in knot theory.Index of a subfactorUsually M is taken to be a… … 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
Morita equivalence — In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring theoretic properties. It is named after Japanese mathematician Kiiti Morita who defined equivalence and a similar notion of duality in 1958.… … Wikipedia
Hochschild homology — In mathematics, Hochschild homology is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain functors. Definition of Hochschild homology of algebras Let k be a ring, A an associative k… … Wikipedia
Connection (algebraic framework) — Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections on modules are generalization of a linear connection on a smooth vector bundle written as a… … Wikipedia
Dual d'un module — En algèbre commutative et plus généralement en théorie des anneaux, le dual d un module A par rapport à un module B (sur un anneau R) est l ensemble des homomorphismes de A dans B. Il est noté Hom(A,B). Si le module B n est pas spécifié, par… … Wikipédia en Français
