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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • [1] C. Chevalley, Fundamental concepts of algebra, Academic Press, New York, 1956. MR 18, 553. MR 0082459 (18:553a)
  • [2] I. Y. Chung, Derivation modules of free joins and $ \mathfrak{m}$-adic completions of algebras, Proc. Amer. Math. Soc. 34 (1972), 49-56. MR 0296061 (45:5122)

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Keywords: Tensor product, subtensor product, graded module, graded algebra, anticommutative algebra, coproduct, category
Article copyright: © Copyright 1973 American Mathematical Society

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