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

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

Auslander–Buchsbaum formula, complete intersection, depth formula, quasi-projective dimension/resolution, vanishing of Tor/Ext
Mathematical Subject Classification
Primary: 13D05, 13D07, 13H10
Received: 18 August 2020
Revised: 8 February 2021
Accepted: 11 February 2021
Published: 4 August 2021
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