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 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 ZC₂ but does not satisfy ZC₃ We show that a semigroup with no nonzero nilpotents satisfiesZC_n for all n ≥ 2 and investigate rings that satisfy ZC_n.

Keywords:

• Zero divisors

1991 Mathematics Subject Classification:

• 16U80
• 20M99