Abstract

In [12], 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 <TEX>$\in$</TEX> 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 <TEX>$(M,\;{\leq})$</TEX>. Also <TEX>$T_4(R)$</TEX> is M-quasi-Armendariz when R is reduced and M-Armendariz.

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