Extensions of Rings Having McCoy Condition

[摘要] Let $R$ be an associative ring with unity.Then $R$ is said to be a {it right McCoy ring} when the equation$f(x)g(x)=0$ (over $R[x]$), where $0eq f(x),g(x) in R[x]$,implies that there exists a nonzero element $cin R$ such that$f(x)c=0$. In this paper, we characterize some basic ringextensions of right McCoy rings and we prove that if $R$ is aright McCoy ring, then $R[x]/(x^n)$ isa right McCoy ring for any positive integer $ngeq 2$ .

[学科分类] 数学（综合）

[关键词] right McCoy ring;Armendariz ring;reduced ring;reversible ring;semicommutative ring