On Skew Triangular Matrix Rings

Abstract

Let $α$ be a nonzero endomorphism of a ring $R$, $n$ be a positive integer and $T_n(R, α)$ be the skew triangular matrix ring. We show that some properties related to nilpotent elements of $R$ are inherited by $T_n(R, α)$. Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring $R[x; α]/(x^n)$, where $R[x; α]$ is the skew polynomial ring.