相对于余挠对的Gorenstein同调维数

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (6): 150-156.

相对于余挠对的Gorenstein同调维数

吴德军^*, 袁源

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2023-04-25 出版日期:2024-12-28 发布日期:2025-01-13
通讯作者: 吴德军(1978-),男,甘肃金昌人,博士,教授.Email:wudj@lut.edu.cn
基金资助:
国家自然科学基金(12261056)

Gorenstein homological dimensions with respect to cotosion pairs

WU De-jun, YUAN Yuan

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2023-04-25 Online:2024-12-28 Published:2025-01-13

摘要/Abstract

摘要： 设$\mathscr{C}$是有足够多投射对象和内射对象的Abel范畴,($\mathscr{A}$,$\mathscr{B}$)是$\mathscr{C}$中完备遗传的余挠对. 给出了Abel范畴$\mathscr{C}$中的Gorenstein $\mathscr{A}-\mathscr{B}$对象的定义及等价刻画, 并研究了模范畴中Gorenstein $\mathscr{A}-\mathscr{B}$维数的相关性质.

关键词: 余挠对, Gorenstein $\mathscr{A}-\mathscr{B}$对象, Gorenstein $\mathscr{A}-\mathscr{B}$维数

Abstract: Let $\mathscr{C}$ be an abelian category with enough projectives and injectives and let ($\mathscr{A}$,$\mathscr{B}$) be a complete hereditary cotorsion pair in $\mathscr{C}$. The definition and equivalent characterizations of Gorenstein $\mathscr{A}-\mathscr{B}$ objects in abelian category $\mathscr{C}$ are given. Additionally, the related properties of Gorenstein $\mathscr{A}-\mathscr{B}$ dimensions in module category are studied.

Key words: cotorsion pair, Gorenstein $\mathscr{A}-\mathscr{B}$ object, Gorenstein $\mathscr{A}-\mathscr{B}$ dimension

中图分类号:

O154.2

吴德军, 袁源. 相对于余挠对的Gorenstein同调维数[J]. 兰州理工大学学报, 2024, 50(6): 150-156.

WU De-jun, YUAN Yuan. Gorenstein homological dimensions with respect to cotosion pairs[J]. Journal of Lanzhou University of Technology, 2024, 50(6): 150-156.

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