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 $cin R$ 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.
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机译：在 cite {Mc}中，McCoy证明了如果$ R $是一个交换环，那么只要$ g（x）$是$ R [x] $的零除，在R $中就存在一个非零的$ c 这样$ cg（x）= 0 $。在本文中，首先我们将这个结果扩展到单半环。然后，对于一个id半体的$ M $，我们给出了$ M $-准Armendariz环的一些例子，这些环是拟Armendariz环的推广。对于任何唯一的产品mono半体$ M $和任何严格完全有序的mono半体（$ M， leq $），每个简化的环都是$ M $-准Armendariz。当$ R $减少时，$ T_4（R）$也是$ M $-准Armendariz，而$ M $ -Armendariz也减少。
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