三角矩阵环上的Gorenstein AC-投射模

吉林大学学报(理学版) ›› 2021, Vol. 59 ›› Issue (6): 1361-1367.

三角矩阵环上的Gorenstein AC-投射模

牟婷¹, 王淼¹, 王占平²

1. 西北师范大学数学与统计学院, 兰州 730070; 2. 绍兴文理学院数学系，浙江绍兴 312000

收稿日期:2021-03-01 出版日期:2021-11-26 发布日期:2021-11-26
通讯作者: 王占平 E-mail:359220363@qq.com

Gorenstein AC-Projective Modules over Triangular Matrix Rings

MU Ting¹, WANG Miao¹, WANG Zhanping²

1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China；
2. Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, Zhejiang Province, China

Received:2021-03-01 Online:2021-11-26 Published:2021-11-26

摘要/Abstract

摘要： 考虑三角矩阵环上的Gorenstein AC-投射模. 设T是三角矩阵环, 其中A和B是环, U是(B,A)-双模. 证明: 若_BU是平坦模, U_A是有限生成投射模, 则左T-模M是Gorenstein AC-投射模当且仅当M₁是Gorenstein AC-投射左A-模, φ^M是单同态, 且Coker φ^M是Gorenstein AC-投射左B-模.

关键词: level模, Gorenstein AC-投射模, 三角矩阵环

Abstract: We consider Gorenstein AC-projective modules over triangular matrix rings. Let T be a triangular matrix rings, where A and B are rings and U is a (B,A)-bimodule. We prove that if _BU is a flat module and U_A is a finitely generated projective module, then a le
ft T-module is a Gorenstein AC-projective module if and only if M₁ is a Gorenstein AC-projective left A-module, φM is a monomorphism, and Coker φ^M is a Gorenstein AC-projective left B-module.

Key words: , level module, Gorenstein AC-projective module, triangular matrix ring

中图分类号:

O153.3

牟婷, 王淼, 王占平. 三角矩阵环上的Gorenstein AC-投射模[J]. 吉林大学学报(理学版), 2021, 59(6): 1361-1367.

MU Ting, WANG Miao, WANG Zhanping. Gorenstein AC-Projective Modules over Triangular Matrix Rings[J]. Journal of Jilin University Science Edition, 2021, 59(6): 1361-1367.

[1]	王淼, 王占平. 三角矩阵环上投射余可解的Gorenstein平坦模[J]. 吉林大学学报(理学版), 2021, 59(1): 39-44.
[2]	刘汉超, 徐晓伟. 可逆上三角矩阵上的加性映射[J]. 吉林大学学报(理学版), 2017, 55(01): 79-81.
[3]	王尧，任艳丽. 分次非奇异三角矩阵环[J]. J4, 2004, 42(04): 503-507.
[4]	任艳丽, 王尧. 分次三角矩阵环的性质[J]. J4, 2003, 41(04): 458-462.