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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (11): 42-47.doi: 10.6040/j.issn.1671-9352.0.2024.204

• • 上一篇    

粘合中Abel范畴的小有限维数

王茜1,2,姚海楼1*   

  1. 1.北京工业大学数学统计学与力学学院, 北京 100124;2.四川文理学院数学学院, 四川 达州 635000
  • 发布日期:2025-11-11
  • 通讯作者: 姚海楼(1963— ),男,教授,博士生导师,博士,研究方向为同调代数与代数表示论. E-mail:yaohl@bjut.edu.cn
  • 作者简介:王茜(1990— ),女,博士研究生,研究方向为同调代数与范畴理论. E-mail:xwang1233@163.com
  • 基金资助:
    国家自然科学基金资助项目(12071120)

Small finitistic dimension of Abel category in a recollement

WANG Xi1,2, YAO Hailou1*   

  1. 1. School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China;
    2. College of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, Sichuan, China
  • Published:2025-11-11

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摘要： 令A是Abel范畴,在A中引入FT-内射对象以及FT-内射维数,讨论FT-内射对象以及FT-内射维数的基本性质。另外,借助FT-内射维数,刻画A的小有限维数f PDA,并且在Abel范畴的粘合中给出3个Abel范畴的f PD维数之间的大小关系。

关键词: 有限投射分解, 小有限维数, FT-内射对象, 粘合

Abstract: Let A be an Abel category. The concept of FT-injective objects and the FT-injective dimension are introduced in A, and the basic properties of FT-injective objects and the FT-injective dimension are discussed. Additionally, using the FT-injective dimension, the small finitistic dimension of A, denoted as f PDA is characterized. The relationship among the small finitistic dimensions of three different Abel categories in a recollement is explored.

Key words: finite projective resolution, small finitistic dimension, FT-injective object, recollement

中图分类号: 

  • O154.2
[1] BASS H. Finitistic dimension and a homological generalization of semiprimary rings[J]. Transactions of the American Mathematical Society, 1960, 95:466-488.
[2] GLAZ S. Commutative coherent rings[M]. Berlin: Springer, 1989:55-63.
[3] 孙小武. FT-内射模与FT-平坦模[D]. 成都:四川师范大学,2015. SUN Xiaowu. FT-injective modules and FT-flat modules[D]. Chengdu: Sichuan Normal University, 2015.
[4] ZHANG Xiaolei, WANG Fanggui. The small finitistic dimensions of commutative rings[J]. Journal of Commutative Algebra, 2023, 15(1):131-138.
[5] WANG F G, ZHOU D H, KIM H, et al. Every Prüfer ring does not have small finitistic dimension at most one[J]. Communications in Algebra, 2020, 48(12):5311-5320.
[6] WANG Fanggui, ZHOU Dechuan, CHEN Dan. Module-theoretic characterizations of the ring of finite fractions of a commutative ring[J]. Journal of Commutative Algebra, 2022, 14(1):141-154.
[7] 章璞. 三角范畴与导出范畴[M]. 北京:科学出版社,2015:409-440. ZHANG Pu. Trangulated categories and derived categories[M]. Beijing: Science Press, 2015:409-440.
[8] HILTON P, STAMMBACH U. A course in homological algebra[M]. New York: Springer, 1997:40-83.
[9] POPESCU N. Abelian categories with applications to rings and modules[M]. London-New York: Academic Press, 1973:16-63.
[10] PSAROUDAKIS C. Homological theory of recollements of abelian categories[J]. Journal of Algebra, 2014, 398:63-110.
[11] PSAROUDAKIS C, VITÓRIA J. Recollements of module categories[J]. Applied Categorical Structures, 2014, 22(4):579-593.
[12] FRANJOU V, PIRASHVILI T. Comparison of abelian categories recollements[J]. Documenta Mathematica, 2004, 9:41-56.
[13] 姚海楼,冯瑶瑶. 阿贝尔范畴粘合上的表现维数[J]. 北京工业大学学报,2019,45(8):809-814. YAO Hailou, FENG Yaoyao. Presented dimensions on recollements of Abelian categories[J]. Journal of Beijing University of Technology, 2019, 45(8):809-814.
[1] 冯瑶瑶,姚海楼. 阿贝尔范畴粘合上的有限表现维数[J]. 《山东大学学报(理学版)》, 2019, 54(2): 89-94.
[2] 朱焱,侯建锋,王纪辉 . 图的粘合运算与韧度和孤立韧度的关系[J]. J4, 2006, 41(5): 59-62 .
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