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Research Article | Open Access

The finiteness of relative homological dimensions

Pei Luo( ), Junjie Zhang
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
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Abstract

Let R be an Artin algebra, m o d R be the category of finitely generated right R-modules, and let F be a sub-bifunctor of E x t R 1 ( − , − ). In this paper, we introduce the notion of the F-extension dimension for m o d R. We further establish the relationships for the finiteness among the F-extension dimension, F-finitistic dimension and F-Igusa-Todorov dimension.

Keywords

relative extension dimensionrelative finitistic dimensionrelative Igusa-Todorov dimension

References

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Electronic Research Archive
Volume 34 Issue 7,
July 2026
Pages 4648-4660
DOI: 10.3934/era.2026205

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Cite this article:
Luo P, Zhang J. The finiteness of relative homological dimensions. Electronic Research Archive, 2026, 34(7): 4648-4660. https://doi.org/10.3934/era.2026205

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Received: 02 March 2026
Revised: 09 May 2026
Accepted: 20 May 2026
Published: 15 July 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)