数学研究
數學研究
수학연구
JOURNAL OF MATHEMATICAL STUDY
2006年
1期
32-35
,共4页
商模%完全平坦模%纯子模%V.N.正则环
商模%完全平坦模%純子模%V.N.正則環
상모%완전평탄모%순자모%V.N.정칙배
Factor module%Completely flat%Pure submodule%V.N. regular ring
引进了一新模类-完全平坦模(每一个商模平坦). 并得到了:令M是平坦左R-模,R M是完全平坦模当且仅当R M的所有子模是纯的当且仅当每一个右R-模A是M-平坦的. 同时本文用完全平坦模刻画了V.N. 正则环.
引進瞭一新模類-完全平坦模(每一箇商模平坦). 併得到瞭:令M是平坦左R-模,R M是完全平坦模噹且僅噹R M的所有子模是純的噹且僅噹每一箇右R-模A是M-平坦的. 同時本文用完全平坦模刻畫瞭V.N. 正則環.
인진료일신모류-완전평탄모(매일개상모평탄). 병득도료:령M시평탄좌R-모,R M시완전평탄모당차부당R M적소유자모시순적당차부당매일개우R-모A시M-평탄적. 동시본문용완전평탄모각화료V.N. 정칙배.
In this paper, we introduce the completely flat module class. A letf R-module M is called completely flat module if every factor module of M is flat. Let M is a flat left R-module, we get that R M is a completely flat module iff all submodules of R M are pure or erery right R-module A is M-flat. It is proven that a ring R is V.N. regular iff every factor module of the injective R-module is flat.
