Weakly Semicommutative Rings and Strongly Regular Rings

Abstract

A ring R is called weakly semicommutative ring if for any a, b ∈ R∗ = R {0} with ab = 0, there exists n ≥ 1 such that either a = 0 and aRb = 0 or b = 0 and aRb = 0. In this paper, many properties of weakly semicommutative rings are introduced, some known results are extended. Especially, we show that a ring R is a strongly regular ring if and only if R is a left SF−ring and weakly semicommutative ring.