(V,W,Y)-Gorenstein平坦模

吉林大学学报(理学版) ›› 2026, Vol. 64 ›› Issue (1): 62-0068.

(V,W,Y)-Gorenstein平坦模

吴永珍, 刘铃, 陈文静

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2025-03-28 出版日期:2026-01-26 发布日期:2026-01-26
通讯作者: 陈文静 E-mail:chenwj@nwnu.edu.cn

(V,W,Y)-Gorenstein Flat Modules

WU Yongzhen, LIU Ling, CHEN Wenjing

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2025-03-28 Online:2026-01-26 Published:2026-01-26

摘要/Abstract

摘要： 令R是有单位元的结合环, V和W是左R-模类, Y是右R-模类. 首先, 定义(V,W,Y)-Gorenstein平坦模, 并给出(V,W,Y)-Gorenstein平坦模的一个等价刻画; 其次, 证明在某些条件下该模类关于直和、直和项和满同态的核封闭.

关键词: (V,W,Y)-Gorenstein平坦模, 右W-分解, 直和项

Abstract: Let R be an associative ring with identity, V and W be classes of left R-modules, and Y be classes of right R-modules. Firstly, we define (V,W,Y)-Gorenstein flat modules, and give an equivalent characterization of (V,W,Y)-Gorenstein flat modules. Secondly, we prove that this class is closed with respect to direct sums, direct summands and kernels of epimorphisms under certain conditions.

Key words: , (V,W,Y)-Gorenstein flat module, right W-decomposition, direct summand

中图分类号:

O153.3

吴永珍, 刘铃, 陈文静. (V,W,Y)-Gorenstein平坦模[J]. 吉林大学学报(理学版), 2026, 64(1): 62-0068.

WU Yongzhen, LIU Ling, CHEN Wenjing. (V,W,Y)-Gorenstein Flat Modules[J]. Journal of Jilin University Science Edition, 2026, 64(1): 62-0068.