Semigroups and rings whose zero products commute

Let S be a semigroup with zero 0 and let n ≥ 2. We say that S satisfies for each permutation σ ∈ 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 ≥ 3, then S also satisfies ZC n+1 , but we give an example of a ring R with identity which satisfies...

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Bibliographic Details
Published in:Communications in algebra 1999-01, Vol.27 (6), p.2847-2852
Main Authors: Anderson, D.D., Camillo, Victor
Format: Article
Language:English
Subjects:
Zero divisors
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Summary:Let S be a semigroup with zero 0 and let n ≥ 2. We say that S satisfies for each permutation σ ∈ 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 ≥ 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 satisfiesZC n for all n ≥ 2 and investigate rings that satisfy ZC n .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927879908826596