Abstract
n 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.
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