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具有半交换自同态的环
引用本文:王尧,沈青,任艳丽.具有半交换自同态的环[J].吉林大学学报(理学版),2013,51(6):997-1003.
作者姓名:王尧  沈青  任艳丽
作者单位:1. 南京信息工程大学 数学与统计学院, 南京 210044; 2. 南京晓庄学院 数学与信息技术学院, 南京 211171
摘    要:通过引入半交换自同态的概念, 研究具有半交换自同态的环(简称α-sc环). 对任何a,b∈R, 如果α(a)b=0, 有aRα(b)=0, 则环R的一个自同态α称为半交换的.
给出α-sc环与相关环的关系及α-sc环的一些扩张性质, 证明了: 1) 设α是约化环R的自同态, 则R是α-sc]环当且仅当R[x]/〈xn〉是α-sc环, 其中〈xn〉是由xn生成的理想, n为任何正整数; 2) 设α是环R的自同构, R是对称的右Ore环, 则R是α-sc环当且仅当R的经典右商环Q(R)是α-sc环.

关 键 词:半交换自同态  &alpha  -sc环  &alpha  -shifting环  环的扩张  
收稿时间:2013-02-05

Rings with Semicommutative Endomorphisms
WANG Yao,SHEN Qing,REN Yan li.Rings with Semicommutative Endomorphisms[J].Journal of Jilin University: Sci Ed,2013,51(6):997-1003.
Authors:WANG Yao  SHEN Qing  REN Yan li
Institution:1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;2. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China
Abstract:We investigated the rings with semicommutative endomorphisms, referred to as the α-sc ring, by means of introducing the notion of semicommutative endomorphisms. A endomorphism α of a ring R is called semicommutative if α(a)b=0 implies aRα(b)=0 for any a,b∈R. We discussed the relations between α sc rings and related rings and present some extensions of α sc rings. It is proved
that: 1) if α is a endomorphism of a reduced ring R, then R is α sc if and only if R[x]/〈xn〉 is α-sc, where 〈xn〉is the ideal by xn generated in R and n is any positive integer; 2) if α is an automorphism of R, R is a symmetric right Ore ring, then R is α sc if and only if the classical right quotient ring Q(R) of R is α-sc.
Keywords:semicommutative endomorphism  α-sc ring  α-shifting ring  extensions of ring
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