On quasi-Armendariz modules

Abstract

In this paper, we introduce the concept of a (alpha-) quasi-Armendariz module, principally quasi-Baer module and syudy its some properties. In particular, we show: (1) For an alpha-quasi-Armendariz module M-R, M-R is a principally quasi-Baer module if and only if M[x; alpha](R[x; alpha]) is a principally quasi-Baer module. (2) A necessary and sufficient condition for a trivial extensions to be quasi-Armendariz is obtained. Consequently, new families of quasi-Armendariz rings are presented.