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.