左拟morphic群环的性质  

Properties of Left Quasi-morphic Group Rings

作　　者：黄青鹤[1] 陈建龙[2] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003 [2]东南大学数学系,江苏南京210096

出　　处：《河北大学学报（自然科学版）》2011年第6期581-585,共5页Journal of Hebei University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10971024);江苏省自然科学基金资助项目(2005207);江苏科技大学人才引进基金项目

摘　　要：为了对左拟morphic环进行进一步研究,讨论了左拟morphic群环的性质,并主要给出了以下结论:如果群环RG是一个左拟morphic环,则R是左拟morphic环,G是局部有限群;若G是局部有限群,那么群环RG是左拟morphic环当且仅当对任意的x∈RG,存在G的有限子群H使得x在RH中是左拟morphic的;设G=HK是一个有限子群H与有限子群K的半直积,如果RG是左拟morphic环,那么RK也是左拟morphic环.Some properties of left quasi-morphic group rings were mainly considered in order to do further research on left quasi-morphic rings.The following results were mainly shown.If RG is a left quasi-morphic ring,then R is a left quasi-morphic ring and G is a locally finite group;If G is a locally finite group,RG is a left quasi-morphic ring if and only if for any element x∈RG there exists a finite subgroup H of G such that x is left quasi-morphic in RH.If G=HK is the semidirect product of finite normal subgroup H by finite subgroup K of G,RG is a left quasi-morphic ring implies that PK is also.

关 键 词：左拟morphic元素 左拟morphic环 拟morphic群环 

分 类 号：O153.3[理学—数学]