On Skew Strongly Reversible Rings Relative to a Monoid  

作　　者：Zhaiming PENG Qinqin GU Liang ZHAO 

机构地区：[1]School of Mathematics & Physics,Anhui University of Technology

出　　处：《Journal of Mathematical Research with Applications》2016年第1期43-50,共8页数学研究及应用（英文版）

基　　金：Supported by the Foundation for Young Talents in College of Anhui Province(Grant No.2012SQRL039ZD);the Postgraduate Innovation Foundation of Anhui University of Technology(Grant No.2014163)

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 丨R丨 ≥ 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.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 丨R丨 ≥ 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.

关 键 词：reversible rings skew strongly M-reversible rings skew monoid rings 

分 类 号：O152.7[理学—数学] O151.21[理学—基础数学]