Journal of Mahani Mathematical Research (May 2023)
On skew power series over McCoy rings
Abstract
Let $R$ be a ring with an endomorphism $\alpha$. A ring $R$ is a skew power series McCoy ring if whenever any non-zero power series $f(x)=\sum_{i=0}^{\infty}a_ix^i,g(x)=\sum_{j=0}^{\infty}b_jx^j\in R[[x;\alpha]]$ satisfy $f(x)g(x)=0$, then there exists a non-zero element $c\in R$ such that $a_ic=0$, for all $i=0,1,\ldots$. We investigate relations between the skew power series ring and the standard ring-theoretic properties. Moreover, we obtain some characterizations for skew power series ring $R[[x;\alpha]]$, to be McCoy, zip, strongly \textit{AB} and has Property (A).
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