Quasi-Armendariz Modules

Abstract:

      For a right $R$-module $N$, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that $N_R$ is quasi-Armendariz if and only if $M_m(N)_{M_m(R)}$ is quasi-Armendariz if and only if $T_m(N)_{T_m(R)}$ is quasi-Armendariz, where $M_m(N)$ and $T_m(N)$ denote the $m\times m$ full matrix and the $m\times m$ upper triangular matrix over $N$, respectively. $N_R$ is quasi-Armendariz if and only if $N[x]_{R[x]}$ is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.