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Journal of Applied Mathematics
Volume 2013, Article ID 309392, 7 pages
http://dx.doi.org/10.1155/2013/309392
Research Article

-Skew -McCoy Rings

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 22 April 2013; Revised 3 July 2013; Accepted 10 July 2013

Academic Editor: Baolin Wang

Copyright © 2013 Areej M. Abduldaim and Sheng Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

As a generalization of -skew McCoy rings, we introduce the concept of -skew -McCoy rings, and we study the relationships with another two new generalizations, -skew -McCoy rings and -skew -McCoy rings, observing the relations with -skew McCoy rings, -McCoy rings, -skew Armendariz rings, -regular rings, and other kinds of rings. Also, we investigate conditions such that -skew -McCoy rings imply -skew -McCoy rings and -skew -McCoy rings. We show that in the case where is a nonreduced ring, if is 2-primal, then is an -skew -McCoy ring. And, let be a weak ( )-compatible ring; if is an -skew -McCoy ring, then is -skew -McCoy.