关于斜McCoy环

On Skew McCoy Rings

中文关键词:  McCoy环  斜McCoy环  斜多项式环  斜Armendariz环  刚性环  上三角矩阵环.

英文关键词:McCoy ring  skew McCoy ring  skew polynomial ring  rigid ring  skew Armendariz ring  upper triangular matrix ring.

中文摘要:

      对于环的自同态$\alpha$,作为$\alpha$-刚性环和McCoy 环的推广,引入了$\alpha$-斜McCoy环,并研究了其性质. 证明了若存在正整数$t$使得$\alpha^t=I_R$,则$\alpha$-斜McCoy环$R$上的斜多项式环$R[x;\alpha]$是$\alpha$-斜McCoy环.同时也证明了若$R$是$\alpha$-刚性环,并且$\alpha(1)=1$,则$R[x;\alpha]/\langle x^2\rangle$是$\bar{\alpha}$-斜McCoy环.

英文摘要:

      For a ring endomorphism $\alpha$, we introduce $\alpha$-skew McCoy rings which are generalizations of $\alpha$-rigid rings and McCoy rings, and investigate their properties. We show that if $\alpha^t=I_R$ for some positive integer $t$ and $R$ is an $\alpha$-skew McCoy ring, then the skew polynomial ring $R[x;\alpha]$ is $\alpha$-skew McCoy. We also prove that if $\alpha(1)=1$ and $R$ is $\alpha$-rigid, then $R[x;\alpha]/\langle x^2\rangle$ is $\bar{\alpha}$-skew McCoy.