平凡环扩张上的n-Gorenstein投射模  

n-Gorenstein projective modules over trivial ring extensions

作　　者：张文汇 赵为东 刘立丽 ZHANG Wen-hui;ZHAO Wei-dong;LIU Li-li(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：《西北师范大学学报(自然科学版)》2025年第2期59-63,共5页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12461003)。

摘　　要：设R是环,M是R-R-双模,R■M是环R按双模M的平凡环扩张.研究了模的n-Gorenstein投射性在范畴R-Mod和R M-Mod之间的传递性.在一定条件下,证明了(X,α)是n-Gorenstein投射左R■M-模当且仅当序列M■_(R)M■_(R)X→M■α→M■_(R)X→α→X正合,并Cokerα且Cokerα是n-Gorenstein投射左R-模.Let R be ring,M be R-R-bimodule and R■M be a trivial ring extension of a ring R by an R-R-bimodule M.In this paper,the transitivity of the n-Gorenstein projectivity of modules between the category R-Mod and R■M-Mod is investigated.Under certain conditions,it is proved that(X,α)is an n-Gorenstein projective left R■M-module if and only if the sequence M■_(R)M■_(R)X→M■α→M■_(R)X→α→X is exact,and Cokerαis an n-Gorenstein projective left R-module.

关 键 词：平凡环扩张 n-Gorenstein投射模 强广义相容双模 正合列 

分 类 号：O153.3[理学—数学]