Semigroups and rings whose zero products commute

被引：119

作者：

Anderson, DD ^{[1
]}

Camillo, V ^{[1
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

来源：

COMMUNICATIONS IN ALGEBRA | 1999年 / 27卷 / 06期

关键词：

zero divisors;

D O I：

10.1080/00927879908826596

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a semigroup with zero 0 and let n greater than or equal to 2. We say that S satisfies ZC(n) if a(1) ... a(n) = 0 double right arrow a(sigma(1)) ... a(sigma(n)) = 0 for each permutation sigma is an element of S-n. A ring R satisfies ZC(n) if (R, .) satisfies ZC(n). We show that if S satisfies ZC(n) for a fixed n greater than or equal to 3, then S also satisfies ZC(n+1), but we give an example of a ring R with identity which satisfies ZC(2) but does not satisfy ZC(3). We show that a semigroup with no nonzero nilpotents satisfies ZC(n) for all n greater than or equal to 2 and investigate rings that satisfy ZC(n).

引用

页码：2847 / 2852

页数：6