(n,m)-强投射余可解Gorenstein平坦模  

(n,m)-Strongly projectively coresolved Gorenstein flat modules

作　　者：钟魁晨 张翠萍 秦军霞 ZHONG Kui-chen;ZHANG Cui-ping;QIN Jun-xia(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2023年第2期63-71,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11761060)。

摘　　要：引入(n,m)-强投射余可解Gorenstein平坦模(即(n,m)-强PGF模)的概念,给出它的一些基本性质。证明了如果M是一个(n,m)-强PGF模,则:(1)M的PGF维数PGFd(M)≤m;(2)当1≤i≤m时,M的第i个合冲是(n,m-i)-强PGF模;当i≥m时,M的第i个合冲是(n,0)-强PGF模。其次证明了:如果模M的第d个合冲是(1,m)-强PGF模,则PGFd(M)=k≤d+m,且M是(1,k)-强PGF模。The concept of an(n,m)-strongly projectively coresolved Gorenstein flat module(i.e.(n,m)-strongly PGF module)is introduced,and some basic properties of it are given.It is proved that if M is an(n,m)-strongly PGF module,then(1)PGF dimension of M PGFd(M)≤m;(2)when 1≤i≤m,the ith syzygy of M is(n,m-i)-strongly PGF module;when i≥m,the ith syzygy of M is(n,0)-strongly PGF module.Secondly,it is proved that the dth syzygy of M is(1,m)-strongly PGF module,then PGF d(M)=k≤d+m,and M is(1,k)-strongly PGF module.

关 键 词：PGF模 强PGF模 n-强PGF模 (n m)-强PGF模 

分 类 号：O153.3[理学—数学]