群分次弱正则环的若干性质  

Some properties on group-graded weakly regular rings

作　　者：汪国军[1] 

机构地区：[1]浙江大学数学系,浙江杭州310028

出　　处：《浙江大学学报（理学版）》2006年第4期361-364,371,共5页Journal of Zhejiang University（Science Edition）

基　　金：浙江省自然科学基金资助项目(102028);浙江省教育厅基金资助项目(407101-G202322)

摘　　要：首先引入群分次弱正则环的概念,在此基础上证明了:(1)设G是群,J是K的分次理想,Jσ=Kσ∩J,则K是群分次弱正则环当且仅当J和K/J是群分次弱正则环.(2)假设K是一个环,n是任一正整数,则K是群分次弱正则的当且仅当Mn(K)是群分次弱正则的.如果K是群G分次环,则Ke是K的子环,且1∈Ke(其中e是群G的单位元).得到了群G-分次环K与Ke的一些关系.再者,引进了分次半平坦模的概念,并有如下主要结果:环K是分次弱正则的当且仅当所有右K-模是分次半平坦的.群分次弱正则环推广了群分次正则环,从而得到群分次正则环的相应结果.The concept of group-graded weakly regular ring is introduced. On this basis, it is proved that ： （1） If G is a group, J is a graded ideal of K, Jσ= Kσ ∩ J, then K is a group-graded weakly regular ring if and only if J and K/ J are group-graded weakly regular rings; （2）If K is a ring, n is a positive integer, then K is a group-graded weakly regular ring if and only if Mn （K） is a group-graded weakly regular ring. If K is a group-graded weakly regular ring, then Ke is a subring of K, and 1∈ Ke （e is the unit of group）. Some relations are given on group graded weakly regular ring K and Ke. Next, the concept of graded semiflat module is introduced and proved that K is a group-graded weakly regular ring if and only if all right K module is graded semiflat module. Group-graded weakly regular rings are the generalization of group-graded regular rings, so the result of group-graded regular rings are similiar.

关 键 词：环 正则环 弱正则环 群分次 

分 类 号：O153.3[理学—数学]