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When is the Tensor Product of Algebras Local?

Moss Eisenberg Sweedler
Proceedings of the American Mathematical Society
Vol. 48, No. 1 (Mar., 1975), pp. 8-10
DOI: 10.2307/2040682
Stable URL: http://www.jstor.org/stable/2040682
Page Count: 3
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When is the Tensor Product of Algebras Local?
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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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