Semigroups and rings whose zero products commute

Citation
Dd. Anderson et V. Camillo, Semigroups and rings whose zero products commute, COMM ALGEB, 27(6), 1999, pp. 2847-2852
Citations number
3
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
27
Issue
6
Year of publication
1999
Pages
2847 - 2852
Database
ISI
SICI code
0092-7872(1999)27:6<2847:SARWZP>2.0.ZU;2-L
Abstract
Let S be a semigroup with zero 0 and let n greater than or equal to 2. We s ay 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 r ing R satisfies ZC(n) if (R, .) satisfies ZC(n). We show that if S satisfie s 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 nilp otents satisfies ZC(n) for all n greater than or equal to 2 and investigate rings that satisfy ZC(n).