具有自反条件的环自同态  

Ring endomorphisms with the reflexive condition

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,江苏南京210044 [2]南京晓庄学院数学与信息技术学院,江苏南京211171

出　　处：《东北师大学报（自然科学版）》2013年第3期9-14,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11071097);江苏省教育厅自然科学基金资助项目(11KJB110007)

摘　　要：研究了具有自反条件的环自同态,拓展了自反环的概念,引入α-rf环,讨论其与相关环的关系.证明了若R是半素的α-rf环,则R[x]/〈xn〉是珔α-rf环,其中〈xn〉是由xn生成的理想;对于右Ore环R和环R的自同构α,若R是α-rf环,则R的经典右商环Q(R)是珔α-rf环.推广了Kwak和Lcc的一些研究结果.This note studies rings endomorphisms with the reflexive condition. The notion of a-rt rings, a genera｜izatin of reflexive rings,is introduced,the relations between α-rf rings and related rings are discussed. It is proved that if R is a semiprime a-rf ring,then R[x]/（xn） is an a-rf ring,where （xn） is the ideal generated by xn;For a right Ore ring R with Q its classical right quotient ring and an automorphism a of a ring R, if R is a-rf ring, then Q is also α-rf ring. As consequences, some conclusions of Kwak-Lee were generalized.

关 键 词：自反环 α-rf环 平凡扩张 Dorroh扩张 多项式环 经典右商环 

分 类 号：O153.3[理学—数学]