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Extensions of Rings Having McCoy Condition
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- Journal:
- Canadian Mathematical Bulletin / Volume 52 / Issue 2 / 01 June 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 267-272
- Print publication:
- 01 June 2009
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- Article
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Let
$R$ be an associative ring with unity. Then $R$ is said to be a right McCoy ring when the equation 
$f\left( x \right)g\left( x \right)\,=\,0$ (over 
$R\left[ x \right]$ ), where 
$0\,\ne \,f\left( x \right)$ , 
$g\left( x \right)\,\in \,R\left[ x \right]$ , implies that there exists a nonzero element 
$c\,\in \,R$ such that 
$f\left( x \right)c\,=\,0$ . 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 
$R\left[ x \right]/\left( {{x}^{n}} \right)$ is a right McCoy ring for any positive integer 
$n\,\ge \,2$ .
