What type of study is this?

This is a Quantitative Study study.

October 3, 2025Open Access

Finiteness of homological dimensions of Ext modules

Key Points

The main finding reveals that finiteness in projective dimension of Ext modules relates directly to dimensions of M and N.
Key evidence indicates that if Ext^i has finite projective dimension for 0 ≤ i ≤ Rfd_R M, then dimensions of M and N are closely tied.
Assessment focuses on finitely generated R-modules, particularly examining the implications of homological dimensions.
These findings highlight a critical relationship, suggesting that the homological behavior of one module influences the other.

Abstract

Let R be a commutative Noetherian local ring and let M and N be nonzero finitely generated R-modules. In this paper, we investigate how the finiteness of the homological dimension of Ext modules between M and N affects that of M and N. One of our main result states that if ExtⁱR (M, N) has finite projective dimension for any 0 i RfdR M, where RfdR M is the (large) restricted flat dimension of M, then M has finite projective or injective dimension if and only if N does.

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Cite This Study

Kaito Kimura (Mon,) studied this question.

synapsesocial.com/papers/68e02f40f0e39f13e7fa28bd https://doi.org/https://doi.org/10.48550/arxiv.2508.12843

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