On the Prime Ideal Structure of Tensor Products of Algebras
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0606689,
title = {On the Prime Ideal Structure of Tensor Products of Algebras},
author = {S. Bouchiba and D. E. Dobbs and S. Kabbaj},
journal= {arXiv preprint arXiv:math/0606689},
year = {2007}
}
Comments
28 pages