JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (11): 42-47.doi: 10.6040/j.issn.1671-9352.0.2024.204

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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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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

CLC Number: 

  • O154.2
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[2] YAN Mei-qi, YAO Hai-lou. Pure projective dimensions on recollements of Abelian categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(8): 1-5.
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