Some examples of quasi-Armendariz rings
Bull. Korean Math. Soc. 2007 Vol. 44, No. 3, 407-414
Printed September 1, 2007
Ebrahim Hashemi
Shahrood University of Technology
Abstract : In \cite{Mc}, McCoy proved that if $R$ is a commutative ring, then whenever $g(x)$ is a zero-divisor in $R[x]$, there exists a nonzero $c\in R$ such that $cg(x)=0$. In this paper, first we extend this result to monoid rings. Then for a monoid $M$, we give some examples of $M$-quasi-Armendariz rings which are a generalization of quasi-Armendariz rings. Every reduced ring is $M$-quasi-Armendariz for any unique product monoid $M$ and any strictly totally ordered monoid ($M,\leq $). Also $T_4(R)$ is $M$-quasi-Armendariz when $R$ is reduced and $M$-Armendariz.
Keywords : Armendariz rings, quasi-Armendariz rings, monoid rings, unique product monoid rings
MSC numbers : 16S36, 16N60, 16P60
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