On Semicommutative Modules and Rings


Agayev N., Harmanci A.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.47, no.1, pp.21-30, 2007 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2007
  • Title of Journal : KYUNGPOOK MATHEMATICAL JOURNAL
  • Page Numbers: pp.21-30

Abstract

We say a module M R a semicommutative module if for any m 2 M and any a epsilon 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 M-R be a p.p.-module, then M-R is a semicommutative module iff M-R is an Armendariz module. For any ring R, R is semicommutative iff A (R,alpha) is semicommutative. Let R be a reduced ring, it is shown that for number n >= 4 and k = [n = 2]; T-n(k) (R) is semicommutative ring but T-n(k-1) (R) is not.