Quasi-projective dimension
Commutative Algebra
2021-08-18 v2
Abstract
In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the following. (1) Over a quotient of a regular local ring by a regular sequence, every finitely generated module has finite quasi-projective dimension. (2) The Auslander--Buchsbaum formula and the depth formula for modules of finite projective dimension remain valid for modules of finite quasi-projective dimension. (3) Several results on vanishing of Tor and Ext hold for modules of finite quasi-projective dimension.
Cite
@article{arxiv.1912.10421,
title = {Quasi-projective dimension},
author = {Mohsen Gheibi and David A. Jorgensen and Ryo Takahashi},
journal= {arXiv preprint arXiv:1912.10421},
year = {2021}
}
Comments
Final version, to appear in Pacific Journal of Mathematics