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. The module construction is analogous to the construction of the tensor product of vector spaces, but can be carried out for a pair of modules over a commutative ring resulting in a third module, and also for a pair of a left-module and a right-module over any ring, with result an abelian group.

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  • 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. The module construction is analogous to the construction of the tensor product of vector spaces, but can be carried out for a pair of modules over a commutative ring resulting in a third module, and also for a pair of a left-module and a right-module over any ring, with result an abelian group. Tensor products are important in areas of abstract algebra, homological algebra, algebraic topology and algebraic geometry. The universal property of the tensor product of vector spaces extends to more general situations in abstract algebra. It allows the study of bilinear or multilinear operations via linear operations. The tensor product of an algebra and a module can be used for extension of scalars. For a commutative ring, the tensor product of modules can be iterated to form the tensor algebra of a module, allowing one to define multiplication in the module in a universal way.
  • Le produit tensoriel de deux modules est une construction en théorie des modules qui à deux modules sur un même anneau assigne un module. C'est une construction abstraite qui est plus simple à assimiler en se limitant dans un premier temps au cas des espaces vectoriels. Le produit tensoriel est très important dans le domaine de la topologie algébrique et de la géométrie algébrique. Le produit tensoriel permet en outre de ramener l'étude d'applications bilinéaires ou multilinéaires à des applications linéaires.
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  • 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. The module construction is analogous to the construction of the tensor product of vector spaces, but can be carried out for a pair of modules over a commutative ring resulting in a third module, and also for a pair of a left-module and a right-module over any ring, with result an abelian group.
  • Le produit tensoriel de deux modules est une construction en théorie des modules qui à deux modules sur un même anneau assigne un module. C'est une construction abstraite qui est plus simple à assimiler en se limitant dans un premier temps au cas des espaces vectoriels. Le produit tensoriel est très important dans le domaine de la topologie algébrique et de la géométrie algébrique.
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  • Tensor product of modules
  • Produit tensoriel de deux modules
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