具有半交换自同态的环  

Rings with Semicommutative Endomorphisms

作　　者：王尧[1] 沈青[1] 任艳丽[2] 

机构地区：[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

出　　处：《吉林大学学报（理学版）》2013年第6期997-1003,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11071097);江苏省自然科学基金(批准号:11KJB110007)

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珔-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珔-sc环.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 a--sc,where 〈x^n〉is the ideal by x^n 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 a--sc.

关 键 词：半交换自同态 α-sc环 α-shifting环 环的扩张 

分 类 号：O153.3[理学—数学]