Skew Armendariz Property of A Class of Upper Triangular Matrix Rings

Abstract:

      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 $R[x; \alpha]$, 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.