Vol. 312, No. 1, 2021

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Quasi-projective dimension

Mohsen Gheibi, David A. Jorgensen and Ryo Takahashi

Vol. 312 (2021), No. 1, 113–147
Abstract

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.

Dedicated to Professors Roger and Sylvia Wiegand on the occasion of their 150th birthday

Keywords
Auslander–Buchsbaum formula, complete intersection, depth formula, quasi-projective dimension/resolution, vanishing of Tor/Ext
Mathematical Subject Classification
Primary: 13D05, 13D07, 13H10
Milestones
Received: 18 August 2020
Revised: 8 February 2021
Accepted: 11 February 2021
Published: 4 August 2021
Authors
Mohsen Gheibi
Department of Mathematics
Florida A&M University
Tallahassee, FL
United States
David A. Jorgensen
Department of Mathematics
University of Texas at Arlington
Arlington, TX
United States
Ryo Takahashi
Graduate School of Mathematics
Nagoya University
Chikusaku, Nagoya
Japan