Commutativity Conditions for Rings and Generalized 2-CN Rings

• 作者: Hua Yao Jianhua Sun Junchao Wei
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 51-62
• 页数: 12页
• 语种: 英文
• DOI: 10.1142/S1005386721000067

摘要

Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions: (1) if for each x ∈ R\N(R) and each y ∈ R,(xy)k =xkyk for k =m,m + 1,n,n + 1,where m and n are relatively prime positive integers,then R is commutative;(2) if for each x ∈ R\J(R) and each y ∈ R,(xy)k =ykxk for k =m,m+ 1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented.