| 三角矩阵环上的Gorenstein AC-投射模 |
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| 引用本文： | 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. |
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| 作者姓名： | 牟婷 王淼 王占平 |
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| 作者单位： | 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 |
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| 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, UA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, φM是单同态, 且Coker φM是Gorenstein AC-投射左B-模.
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| 关 键 词： | level模 Gorenstein AC-投射模 三角矩阵环 |
| 收稿时间： | 2021-03-01 |
Gorenstein AC-Projective Modules over Triangular Matrix Rings |
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| MU Ting,WANG Miao,WANG Zhanping.Gorenstein AC-Projective Modules over Triangular Matrix Rings[J].Journal of Jilin University: Sci Ed,2021,59(6):1361-1367. |
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| Authors: | MU Ting WANG Miao WANG Zhanping |
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| Institution: | 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
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| 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 UA 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 φM is a Gorenstein AC-projective left B-module. |
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| Keywords: | level module Gorenstein AC-projective module triangular matrix ring |
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