On the prime ideal structure of tensor products of algebras

Samir Bouchiba; David E. Dobbs; Salah Eddine Kabbaj

doi:10.1016/S0022-4049(02)00067-1

On the prime ideal structure of tensor products of algebras

Samir Bouchiba, David E. Dobbs, Salah Eddine Kabbaj^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English
Pages (from-to)	89-112
Number of pages	24
Journal	Journal of Pure and Applied Algebra
Volume	176
Issue number	2-3
DOIs	https://doi.org/10.1016/S0022-4049(02)00067-1
State	Published - 24 Dec 2002
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/S0022-4049(02)00067-1

Cite this

@article{e25e5cf480a041e9ac9579c6f65c51f1,

title = "On the prime ideal structure of tensor products of algebras",

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.",

author = "Samir Bouchiba and Dobbs, \{David E.\} and Kabbaj, \{Salah Eddine\}",

year = "2002",

month = dec,

day = "24",

doi = "10.1016/S0022-4049(02)00067-1",

language = "English",

volume = "176",

pages = "89--112",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

number = "2-3",

}

TY - JOUR

T1 - On the prime ideal structure of tensor products of algebras

AU - Bouchiba, Samir

AU - Dobbs, David E.

AU - Kabbaj, Salah Eddine

PY - 2002/12/24

Y1 - 2002/12/24

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0037168440

U2 - 10.1016/S0022-4049(02)00067-1

DO - 10.1016/S0022-4049(02)00067-1

M3 - Article

AN - SCOPUS:0037168440

SN - 0022-4049

VL - 176

SP - 89

EP - 112

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 2-3

ER -

On the prime ideal structure of tensor products of algebras

Abstract

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this