|ISSN 1088-6826(online) ISSN 0002-9939(print)|
Direct decomposition of tensor products into subtensor products
Abstract: A subtensor product of a family of modules is defined by using a subdirect product of the family of modules considered as sets. A tensor product of modules can be decomposed into a direct sum of subtensor products of the modules. Subtensor products of graded modules and graded algebras are also studied. As an application of these, a certain subtensor product of a family (not necessarily finite) of anticommutative algebras is shown to be a coproduct of this family in the category of unitary anticommutative algebras, and it can be imbedded as a direct summand into a tensor product of the family as modules.
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