On the Strong (A)-Rings of Mahdou and Hassani

被引：9

作者：

Dobbs, David E. ^{[1
]}

Shapiro, Jay ^{[2
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] George Mason Univ, Dept Math, Fairfax, VA 22030 USA

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2013年 / 10卷 / 04期

关键词：

Commutative ring; Property A; zero-divisor; annihilator; prime ideal; associated prime; Noetherian; finite ring; integral domain;

D O I：

10.1007/s00009-013-0276-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A (commutative unital) ring R with only finitely many minimal prime ideals (for instance, a Noetherian ring) is reduced and a strong (A)-ring if and only if R is an integral domain. Thus, the smallest reduced ring which has Property A but is not a strong (A)-ring is . A Noetherian ring R is a strong (A)-ring if and only if Ass (R) (R) has a unique maximal element.

引用

页码：1995 / 1997

页数：3