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Quasi-projective
dimension
Mohsen Gheibi, David A. Jorgensen and Ryo Takahashi |
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Vol. 312 (2021), No. 1, 113–147
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Abstract |
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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. |
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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
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Mathematical Subject Classification
Primary: 13D05, 13D07, 13H10
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Milestones
Received: 18 August 2020
Revised: 8 February 2021
Accepted: 11 February 2021
Published: 4 August 2021
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Authors |
| Mohsen Gheibi | |
| Department of Mathematics Florida A&M University Tallahassee, FL United States |
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| David A. Jorgensen | |
| Department of Mathematics University of Texas at Arlington Arlington, TX United States |
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| Ryo Takahashi | |
| Graduate School of Mathematics Nagoya University Chikusaku, Nagoya Japan |
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