Extensions of Rings Having McCoy Condition

Koşan, Muhammet Tamer

Canadian mathematical bulletin, Tome 52 (2009) no. 2, pp. 267-272

Résumé

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 $n\,\ge \,2$ .

Détail

DOI : 10.4153/CMB-2009-029-5

Mots-clés : 16D10, 16D80, 16R50, right McCoy ring, Armendariz ring, reduced ring, reversible ring, semicommutative ring