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arXiv · 1912.10421

Quasi-projective dimension

Mohsen Gheibi·David A. Jorgensen·Ryo Takahashi
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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.

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Mohsen Gheibi, David A. Jorgensen, Ryo Takahashi. 2021-02-12. Quasi-projective dimension. https://doi.org/10.2140/pjm.2021.312.113

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