Rings with annihilator condition and their extensions
DOI:
https://doi.org/10.13069/jacodesmath.v11i2.260Keywords:
Annihilator condition, Annihilators, p.q.-Baer rings, $\alpha$-skew quasi Armendariz ringsAbstract
Let $R$ be an associative unital ring and $\alpha$ an endomorphism of $R$. In this article, we aim to investigate rings that satisfy Property $(a.c.)$ and explore some related rings. Moreover, we examine many polynomial extensions of $R$ satisfying Property $(a.c.)$. In particular, $\alpha$-skew quasi-Armendariz rings and $\alpha$-(sps) quasi-Armendariz rings. We prove that this class of rings has always Property $(a.c.)$ on the left but not necessarily on the right. Furthermore, we investigate the transmission of Property $(a.c)$ from a ring $R$ to $R[x,\alpha]$ and $R[[x,\alpha]]$.
Received: 1 September 2022 | Accepted: 4 July 2023Downloads
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