Semigroups and rings whose zero products commute

Abstract

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 ZCn if (.R, .) satisfies ZCn. We show that if S satisfies ZCn for a fixed n ≥ 3, then S also satisfies ZCn+1, but we give an example of a ring R with identity which satisfies ZC2 but does not satisfy ZC3 We show that a semigroup with no nonzero nilpotents satisfiesZCn for all n ≥ 2 and investigate rings that satisfy ZCn.