On weak $α$-skew McCoy Rings

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

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