发表机构
Bengbu University; Yangzhou University; Zhejiang Shuren University（蚌埠学院; 扬州大学; 浙江树人大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过建立$\ast$-可逆环的新刻画并证明其与$\ast$-对称环等价，引入pro-$\ast$-可逆环与nil-$\ast$-可逆环两类广义$\ast$-可逆环，研究其性质、相互关系并构造区分例子。
AI 中文摘要
设$R$为$\ast$-环，其中$a,b\in R$。称环$R$为$\ast$-可逆的，若$ab=0$蕴含$b^{\ast}a=0$。本文首先建立了$\ast$-可逆环与可逆环的若干新刻画。特别地，我们证明了$\ast$-可逆环与$\ast$-对称环一致。利用这些刻画，我们引入了两类广义$\ast$-可逆环：pro-$\ast$-可逆环与nil-$\ast$-可逆环。称环$R$为pro-$\ast$-可逆的，若$ab\in P(R)$蕴含$b^{\ast}a\in P(R)$；称$R$为nil-$\ast$-可逆的，若对每个$c\in N(R)$，$cb=0$推出$b^{\ast}c=0$且$cb^{\ast}=0$。我们研究了pro-$\ast$-可逆环与nil-$\ast$-可逆环的基本性质与刻画，考虑了所有这些环类之间的相互关系，并构造了用以区分这些环的相关例子。
英文摘要
Let $R$ be a $\ast$-ring with $a,b\in R$. A ring $R$ is said to be $\ast$-reversible if $ab=0$ implies $b^{\ast}a=0$. In this paper, we first establish several new characterizations of $\ast$-reversible rings and reversible rings. In particular, we prove that $\ast$-reversible rings coincide with $\ast$-symmetric rings. Using these characterizations, we introduce two new classes of generalized $\ast$-reversible rings: pro-$\ast$-reversible rings and nil-$\ast$-reversible rings. A ring $R$ is called pro-$\ast$-reversible if $ab\in P(R)$ implies $b^{\ast}a\in P(R)$, and $R$ is nil-$\ast$-reversible if for every $c\in N(R)$, $cb=0$ yields both $b^{\ast}c=0$ and $cb^{\ast}=0$. The basic properties and characterizations of pro-$\ast$-reversible and nil-$\ast$-reversible rings are investigated. The interrelationships among all these ring classes are considered. The related examples to distinguish these rings are constructed.
