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# Extensions of Rings Having McCoy Condition

Published:2009-06-01
Printed: Jun 2009
• Muhammet Tamer Ko\c{s}an
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## Abstract

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 $0\neq f(x),g(x) \in R[x]$, implies that there exists a nonzero element $c\in R$ such that $f(x)c=0$. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if $R$ is a right McCoy ring, then $R[x]/(x^n)$ is a right McCoy ring for any positive integer $n\geq 2$ .
 Keywords: right McCoy ring, Armendariz ring, reduced ring, reversible ring, semicommutative ring
 MSC Classifications: 16D10 - General module theory 16D80 - Other classes of modules and ideals [See also 16G50] 16R50 - Other kinds of identities (generalized polynomial, rational, involution)