On weak Armendariz ideals
Commun. Korean Math. Soc. 2008 Vol. 23, No. 3, 333-342
Printed September 1, 2008
Ebrahim Hashemi
Shahrood University of Technology
Abstract : We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if $I$ is a weak Armendariz ideal of $R$, then $I[x]$ is a weak Armendariz ideal of $R[x]$. As a consequence, we show that, $R$ is weak Armendariz if and only if $R[x]$ is a weak Armendariz ring. Also we obtain a generalization of \cite{Li} and \cite{Liu}.
Keywords : Armendariz rings, weak Armendariz rings, semicommutative rings, weakly semicommutative rings
MSC numbers : 16S50
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