强Prüfer环的同调刻画  

A Homological Characterization of Strong Prüfer Rings

作　　者：王芳贵 乔磊 周德川 Fang Gui WANG;Lei QIAO;De Chuan ZHOU(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,P.R.China;College of Science,Southwest University of Science and Technology,Mianyang 621010,P.R.China)

机构地区：[1]四川师范大学数学科学学院,成都610068 [2]西南科技大学理学院,绵阳621010

出　　处：《数学学报（中文版）》2021年第2期311-316,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11671283,11701398)。

摘　　要：设R是环,R的小finitistic维数定义为fPD(R)=sup{pd_(R)M|M∈FPR}.本文证明了:若R是连通的强Prüfer环,则fPD(R)≤1.也证明了若R是强Prufer环,M∈FPR,且M是Q-挠模,则pd_(R)M≤1.Let R be a commutative ring.Then the small finitistic projective dimension of R is defined as fPD(R)=sup{pd_(R)M|M∈FPR}.In this paper,it is shown that if R is a connected strong Prüfer ring,then fPD(R)≤1.It is also shown that if R is a strong Prüfer ring,and if M is a Q-torsion module with M∈FPR,then pd_(R)M≤1.

关 键 词：有限投射分解 小finitistic维数 Q-挠模 强Prüfer环 连通环 

分 类 号：O154[理学—数学]