形式三角矩阵环上的n-Gorenstein投射模

doi:10.6040/j.issn.1671-9352.0.2021.723

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (10): 44-49.doi: 10.6040/j.issn.1671-9352.0.2021.723

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形式三角矩阵环上的n-Gorenstein投射模

牛韶花,杨刚

兰州交通大学数理学院, 甘肃兰州 730070

发布日期:2022-10-06
作者简介:牛韶花(1996— ), 女, 硕士研究生, 研究方向为同调代数. E-mail:2537194227@qq.com
基金资助:
国家自然科学基金资助项目(12161049);兰州交通大学“百名青年优秀人才培养计划”基金资助项目;甘肃省自然科学基金资助项目(21JR7RA295)

n-Gorenstein projective modules over formal triangular matrix rings

NIU Shao-hua, YANG Gang

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Published:2022-10-06

摘要/Abstract

摘要： 设n是整数,T=(A 0U B)是形式三角矩阵环,其中A,B是环,U是左B右A双模,_BU是投射模,U_A的平坦维数有限。证明了若左T-模(M₁M₂)_φ^M是n-Gorenstein投射模,则M₁是(n-1)-Gorenstein投射左A-模,M₂/Im(φ^M)是n-Gorenstein投射左B-模,并且 φ^M:U⊗_AM₁→M₂是单射。反过来,若M₁是n-Gorenstein投射左A-模,M₂/Im(φ^M)是n-Gorenstein投射左B-模,并且 φ^M:U⊗_AM₁→M₂是单射,则左T-模(M₁M₂)_φ^M是n-Gorenstein投射模。

关键词: n-Gorenstein投射模, 形式三角矩阵环, 伴随对

Abstract: Let n be an integer, T=(A 0U B) a formal triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule, _BU is projective, U_A has finite flat dimension. It is proved that, if a left T-module (M1M2)_φ^M is n-Gorenstein projective, then M1 is (n-1)-Gorenstein projective in A-Mod, M₂/Im(φ^M)is n-Gorenstein projective in B-Mod, and φ^M:U⊗_AM1→M2 is a monomorphism. Conversely, if M1 is n-Gorenstein projective in A-Mod, M₂/Im(φ^M) is n-Gorenstein projective in B-Mod, and φ^M:U⊗_AM1→M2 is a monomorphism, then the left T-module (M1M2)_φ^M is n-Gorenstein projective.

Key words: n-Gorenstein projective module, formal triangular matrix ring, adjoint pair

中图分类号:

O154.2

牛韶花,杨刚. 形式三角矩阵环上的n-Gorenstein投射模[J]. 《山东大学学报(理学版)》, 2022, 57(10): 44-49.

NIU Shao-hua, YANG Gang. n-Gorenstein projective modules over formal triangular matrix rings[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(10): 44-49.

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形式三角矩阵环上的n-Gorenstein投射模

n-Gorenstein projective modules over formal triangular matrix rings

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