斜Armendariz矩阵环

On Skew Armendariz Matrix Rings

中文关键词:  Armendariz环  斜Armendariz环  约化环  矩阵环.

英文关键词:Armendariz ring  skew Armendariz ring  reduced ring  matrix ring.

中文摘要:

      设$R$是环.本文证明了上三角矩阵环$T_n(R)$的子环$U_n(R)$是$\overline{\alpha}$-斜Armendariz环当且仅当$R$是$\alpha$-刚性环，同时也指出$U_n(R)$是一些非$\overline{\alpha}$-斜Armendariz矩阵环的极大Armendariz子环，其中$\alpha: R\rightarrow R$是保持单位元的环同态.

英文摘要:

      Let $R$ be a ring. We show in the paper that the subring $U_n(R)$ of the upper triangular matrix ring $T_n(R)$ is $\overline{\alpha}$-skew Armendariz if and only if $R$ is $\alpha$-rigid, also it is maximal in some non $\overline{\alpha}$-skew Armendariz rings, where $\alpha$ is a ring endomorphism of $R$ with $\alpha(1)=1$.