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When is the Tensor Product of Algebras Local?

Name: When is the Tensor Product of Algebras Local?
Creator: Moss Eisenberg Sweedler
Keywords: Transcendental field extensions, Algebraic field extensions, Multilinear algebra, tensor calculus, 8. Economic growth, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), 0101 mathematics, 01 natural sciences, Local rings and semilocal rings

When is the tensor product of algebras local?

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1975Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 48, page 8 (issn: 0002-9939,

Authors: Moss Eisenberg Sweedler;

doi: 10.2307/2040682 , 10.1090/s0002-9939-1975-0360568-6

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. Introduction. Throughout A and B are commutative algebras over a field

Keywords

Transcendental field extensions, Algebraic field extensions, Multilinear algebra, tensor calculus, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), Local rings and semilocal rings

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