幺半群上的斜强可逆环

On Skew Strongly Reversible Rings Relative to a Monoid

中文关键词:  可逆环  斜强$M$-可逆环  斜半群环

英文关键词:reversible rings  skew strongly $M$-reversible rings  skew monoid rings

中文摘要:

      对于幺半群$M$, 本文介绍了强$M$-可逆环的推广斜强$M$-可逆环及其性质. 如果$G$是有限阿贝尔群, 则$G$是无挠的当且仅当存在环$R$, 当$|R|\geq 2$ 时$R$ 是斜强$M$- 可逆环. 如果$R$是有古典右商环$Q$的右Ore环, 则$R$是斜强$M$-可逆当且仅当$Q$是斜强$M$-可逆.

英文摘要:

      For a monoid $M$, we introduce the concept of skew strongly $M$-reversible rings which is a generalization of strongly $M$-reversible rings, and investigate their properties. It is shown that if $G$ is a finitely generated Abelian group, then $G$ is torsion-free if and only if there exists a ring $R$ with $|R| \geq 2$ such that $R$ is skew strongly $G$-reversible. Moreover, we prove that if $R$ is a right Ore ring with classical right quotient ring $Q$, then $R$ is skew strongly $M$-reversible if and only if $Q$ is skew strongly $M$-reversible.