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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

When is the tensor product of algebras local?


Author: Moss Eisenberg Sweedler
Journal: Proc. Amer. Math. Soc. 48 (1975), 8-10
DOI: https://doi.org/10.1090/S0002-9939-1975-0360568-6
MathSciNet review: 0360568
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Abstract: Suppose the tensor product of two commutative algebras over a field is local. It is easily shown that each of the commutative algebras is local and that the tensor product of the residue fields is local. Moreover, one of the algebras must be algebraic over the ground field, i.e. contain no transcendentals. These three conditions characterize when the tensor product of commutative algebras is local.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0360568-6
Article copyright: © Copyright 1975 American Mathematical Society