一类上三角矩阵环$W_{n}(p, q)$的斜Armendariz性质

设α是环R的一个自同态,称环R是α-斜Armendariz环,如果在Rx;α]中,(∑_(i=0)~ma_ix~i)(∑_(j=0)~nb_jx~j)=0,那么a_ia~i(b_j)=0,其中0≤i≤m,0≤j≤n.设R是α-rigid环,则R上的上三角矩阵环的子环W_n(p,q)是α~—-斜Armendariz环.

Skew Armendariz Property of A Class of Upper Triangular Matrix Rings

Let $\alpha$ be an endomorphism of a ring $R$. A ring $R$ is called $\alpha$-skew Armendariz, if $(\sum_{i=0}^{m}a_{i}x^{i})$\\$(\sum_{j=0}^{n}b_{j}x^{j})=0$ in $Rx; \alpha]$, then $a_{i}\alpha^{i}(b_{j})=0$, where Let $\alpha$ be an endomorphism of a ring $R$. A ring $R$ is called $\alpha$-skew Armendariz, if $(\sum_{i=0}^{m}a_{i}x^{i})$\\$(\sum_{j=0}^{n}b_{j}x^{j})=0$ in $Rx; \alpha]$, then $a_{i}\alpha^{i}(b_{j})=0$, where Let $\alpha$ be an endomorphism of a ring $R$. A ring $R$ is called $\alpha$-skew Armendariz, if $(\sum_{i=0}^{m}a_{i}x^{i})$\\$(\sum_{j=0}^{n}b_{j}x^{j})=0$ in $Rx; \alpha]$, then $a_{i}\alpha^{i}(b_{j})=0$, where $0\leq i\leq m, 0\leq j\leq n$. Let $R$ be $\alpha$-rigid. Then a class of subrings $W_{n}(p, q)$ of upper triangular matrix rings are $\overline{\alpha}$-skew Armendariz.