Frobenius双模和相对n-Gorenstein投射模  

Frobenius bimodules and relative nGorenstein projective modules

作　　者：张文汇 刘立丽 ZHANG Wen-hui;LIU Li-li(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《兰州大学学报（自然科学版）》2024年第2期243-247,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(11861055)。

摘　　要：设R和S均是环,SMR是一Frobenius双模,MR是生成子.χ是一左R-模类,y是一左S-模类.在一定条件下,证明左R-模X是n-X-Gorenstein投射模当且仅当M■RX是n-y-Gorenstein投射左S-模.进而证明当F:RM→SM是忠实的Frobenius函子时,n-GX-pdR(X)=n-Gy-pdS(F(X)).Let R and S be ring_(s)M_(R)be a Frobenius bimodule with generator M_(p)Let x be a class of left R-modules and y a class of left S-modules.Under some conditions,it was proved that a left R-module X is n-X-Gorenstein projective if and only if M■X is a n-y-Gorenstein projective left S module.We also proved that if F:_(R)M→s_(M)is a faithful Frobenius functor,then n-GX-pdR(X)=n-Gy-pdS(F(X)).

关 键 词：Frobenius双模 n-X-Gorenstein投射R-模 Frobenius函子 

分 类 号：O153.3[理学—数学]