On Semicommutative Modules and Rings

Abstract

We say a module MR a semicommutative module if for any m 2 M and any a 2 R, ma = 0 implies mRa = 0. This paper gives various properties of reduced, Armendariz, Baer, Quasi-Baer, p:p: and p:q:-Baer rings to extend to modules. In addition we also prove, for a p.p.-ring R, R is semicommutative iff R is Armendariz. Let R be an abelian ring and MR be a p:p:-module, then MR is a semicommutative module iff MR is an Armendariz module. For any ring R, R is semicommutative iff A(R; ®) is semicommutative. Let R be a reduced ring, it is shown that for number n ¸ 4 and k = [n=2]; Tk n (R) is semicommutative ring but Tk¡1 n (R) is not.