形式三角矩阵环上的Clean-投射模与Clean-奇点范畴

吉林大学学报(理学版) ›› 2026, Vol. 64 ›› Issue (5): 1013-1020.

形式三角矩阵环上的Clean-投射模与Clean-奇点范畴

闫美琪¹, 姚海楼²

1. 太原师范学院数学与统计学院, 太原 030619； 2. 北京工业大学数学统计学与力学学院, 北京 100124

收稿日期:2026-02-05 出版日期:2026-09-26 发布日期:2026-09-26
通讯作者: 姚海楼 E-mail:yaohl@bjut.edu.cn

Clean-Projective Modules and Clean-Singularity Categories over Formal Triangular Matrix Rings

Yan Meiqi¹, Yao Hailou²#br#

#br#

1. College of Mathematics and Statistics, Taiyuan Normal University, Taiyuan 030619, China；
2. School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China

Received:2026-02-05 Online:2026-09-26 Published:2026-09-26

摘要/Abstract

摘要： 设T是形式三角矩阵环. 首先, 考虑T上的clean-投射模, 证明若左T-模(X,Y)_φ是clean-投射模, 则X/(Im φ)是clean-投射左R-模, Y是clean-投射左S-模；其次, 分别构造T上的clean-导出范畴和clean-奇点范畴的粘合.

关键词: 形式三角矩阵环, clean-投射模, clean-奇点范畴, 粘合

Abstract: Let T be a formal triangular matrix ring. First, this paper investigates clean-projective modules over T, and proves that if a left T-module (X,Y)_φ is clean-projective, then X/(Im φ) is a clean-projective left R-module and Y is a clean-projective left S-module. Second, the recollements for clean-derived categories and clean-singularity categories over T are constructed separately.

Key words: formal triangular matrix ring, clean-projective module, clean-singularity category, recollement

中图分类号:

O154.1

闫美琪, 姚海楼. 形式三角矩阵环上的Clean-投射模与Clean-奇点范畴[J]. 吉林大学学报(理学版), 2026, 64(5): 1013-1020.

Yan Meiqi, Yao Hailou. Clean-Projective Modules and Clean-Singularity Categories over Formal Triangular Matrix Rings[J]. Journal of Jilin University Science Edition, 2026, 64(5): 1013-1020.

[1]	熊郑瑶, 赵仁育. 一类形式三角矩阵环上的Ding模[J]. 吉林大学学报(理学版), 2025, 63(6): 1586-1592.
[2]	刘亚楠, 杨刚. 形式三角矩阵环上的F-Gorenstein平坦模[J]. 吉林大学学报(理学版), 2023, 61(5): 1029-1036.