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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
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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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