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Keywords:
ring with right property (A); skew Hurwitz series ring; $\omega $-compatible ring
ring with right property (A); skew Hurwitz series ring; $\omega $-compatible ring
Summary:
A ring $R$ has right (left) property (A) if for every finitely generated two-sided ideal $I\subseteq Z_{l}(R)$ $(I\subseteq Z_{r}(R))$, there exists nonzero $u\in R$ $(v\in R)$ such that $Iu=0$ $(vI=0)$. In this article, we establish a relationship between a ring with property (A) and its skew Hurwitz series ring $(HR, \omega )$, where $\omega $ is an endomorphism of $R$. Also some properties of strongly right AB ring for skew Hurwitz series rings are studied.
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