Properties of quasi-projective dimension over abelian categories
Rings and Algebras
2025-09-25 v1 Commutative Algebra
Category Theory
Abstract
Quasi-projective dimension was introduced by Gheibi, Jorgensen and Takahashi to generalize the Auslander-Buchsbaum formula and the depth formula in commutative algebra. In this paper, we establish some basic properties of quasi-projective dimensions of objects in abelian categories. Analogous to global dimension of rings, we also introduce the concept of quasi-global dimension for left Noetherian rings, and then compare quasi-global dimension with global dimension for a class of Nakayama algebras. This provides new examples of finite-dimensional algebras with finite quasi-global dimensions but infinite global dimensions.
Keywords
Cite
@article{arxiv.2509.20137,
title = {Properties of quasi-projective dimension over abelian categories},
author = {Hongxing Chen and Xiaohu Chen and Mengge Liu},
journal= {arXiv preprint arXiv:2509.20137},
year = {2025}
}
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19 pages