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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Direct decomposition of tensor products into subtensor products


Author: I. Y. Chung
Journal: Proc. Amer. Math. Soc. 37 (1973), 1-9
MSC: Primary 15A72
MathSciNet review: 0366956
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0366956-4
PII: S 0002-9939(1973)0366956-4
Keywords: Tensor product, subtensor product, graded module, graded algebra, anticommutative algebra, coproduct, category
Article copyright: © Copyright 1973 American Mathematical Society