On the Prime Ideal Structure of Tensor Products of Algebras

Details On the Prime Ideal Structure of Tensor Products of Algebras On the Prime Ideal Structure of Tensor Products of Algebras

2006-06-27

arxiv.org/abs/math/0606689v1

J. Pure Appl. Algebra 176 (2002) 89-112

Mathematics

Commutative Algebra

28 pages

Scientific paper

This paper is concerned with the prime spectrum of a tensor product of algebras over a field. It seeks necessary and sufficient conditions for such a tensor product to have the S-property, strong S-property, and catenarity. Its main results lead to new examples of stably strong S-rings and universally catenarian rings. The work begins by investigating the minimal prime ideal structure. Throughout, several results on polynomial rings are recovered, and numerous examples are provided to illustrate the scope and sharpness of the results.

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