Direct decomposition of tensor products into subtensor products

Chung, I. Y.

doi:10.1090/S0002-9939-1973-0366956-4

Direct decomposition of tensor products into subtensor products
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by I. Y. Chung

Proc. Amer. Math. Soc. 37 (1973), 1-9

DOI: https://doi.org/10.1090/S0002-9939-1973-0366956-4

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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.

References

Claude Chevalley, Fundamental concepts of algebra, Academic Press, Inc., New York, 1956. MR 82459
I. Y. Chung, Derivation modules of free joins and $m$-adic completions of algebras, Proc. Amer. Math. Soc. 34 (1972), 49–56. MR 296061, DOI 10.1090/S0002-9939-1972-0296061-6