局部完全环的同调刻画  

Homological Characterizations of Locally Perfect Domains

作　　者：林诗雨 王芳贵 陈丹 LIN Shiyu;WANG Fanggui;CHEN Dan(School of Mathematics and Sciences,Sichuan Normal University,Chengdu 610066,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2021年第4期459-465,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11671283)。

摘　　要：设R是交换环,m∈Max(R).R-模M称为几乎投射模,是指对任意R_(m)-模N,都有Ext_(R)^(1)(M,N)=0.给出Rees定理对于几乎投射维数的一个应用.证明若R模A是非零模且Apd_(R) A<∞,则Apd_(R) A=Apd_(R) A+1,其中R=R/aR,a∈R既不是单位也不是零因子.得到若环R是局部完全环,则AFPD(R)=0.还证明整环R是几乎局部完全整环,当且仅当对任何极大理想m,有R_(m)是几乎完全整环.Let R be a commutative ring.An R-module M is said to be almost projective if Ext_(R)^(1)(M,N)=0 for any R_(m)module,and m of R is a maximal ideal of R.In this paper,We give the change theorem of rings on the almost projective dimensions of R based on its property.The equality that Apd_(R) A=Apd_(R) A+1 is proved when A is nonzero and Apd_(R) A<∞.Moreover,we have we also prove that AFPD(R)=0 when R is a locally perfect ring.R is an almost locally perfect domain if and only if R_(m)is an almost perfect domain,where m of R is any maximal ideal of R.

关 键 词：几乎投射模 换环定理 局部完全环 

分 类 号：O154[理学—数学]