ON WEAK $lpha$-SKEW MCCOY RINGS

摘要

Let $lpha$ be an endomorphism of a ring $R$. We introduce the notion of weak $lpha$-skew McCoy rings which are a generalization of the $lpha$-skew McCoy rings and the weak McCo rings. Some properties of this generalization are established, and connections of properties of a weak $lpha$-skew McCoy ring $R$ with $nimes n$ upper triangular $T_n(R)$ are investigated. We study relationship between the weak skew McCoy property of a ring $R$ and its polynomial ring, $R[x]$. Among applications, we show a number of interesting properties of a weak $lpha$-skew McCoy ring $R$ such as weak skew McCoy property in a ring $R$.