论文标题
可逆的环属性通过iDempotent元素
Reversible ring property via idempotent elements
论文作者
论文摘要
关于愿意元素如何影响戒指可逆性的问题，我们根据基于群体研究了可逆性的版本。从这个角度来看，我们介绍{\ it right}（resp。，{\ it左}）{\ it $ e $ - 可逆环}。我们表明，这个概念不是左右对称性。提供了圆环中正确的$ e $可逆性的基本属性。还证明，如果$ r $是半弹药戒指，则$ r $在$ e $时是正确的，并且仅当它是正确的$ e $时，并且仅当它是$ e $ e $ symmetric时，并且仅当它是正确的$ e $ e $ - $ e $ - sy-Syplemicmutative。另外，对于正确的$ e $ $可逆环$ r $，$ r $是当时是一个质量戒指，仅当它是一个域时。结果表明，正确的$ e $可逆环严格介于$ e $ symmetric戒指和正确的$ e $ $ sepoodmumutative环之间。
Regarding the question of how idempotent elements affect reversible property of rings, we study a version of reversibility depending on idempotents. In this perspective, we introduce {\it right} (resp., {\it left}) {\it $e$-reversible rings}. We show that this concept is not left-right symmetric. Basic properties of right $e$-reversibility in a ring are provided. Among others it is proved that if $R$ is a semiprime ring, then $R$ is right $e$-reversible if and only if it is right $e$-reduced if and only if it is $e$-symmetric if and only if it is right $e$-semicommutative. Also, for a right $e$-reversible ring $R$, $R$ is a prime ring if and only if it is a domain. It is shown that the class of right $e$-reversible rings is strictly between that of $e$-symmetric rings and right $e$-semicommutative rings.
