@article{Luo2026, 
author = {Pei Luo and Junjie Zhang},
title = {The finiteness of relative homological dimensions},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {7},
pages = {4648-4660},
keywords = {relative extension dimension, relative finitistic dimension, relative Igusa-Todorov dimension},
url = {https://www.sciopen.com/article/10.3934/era.2026205},
doi = {10.3934/era.2026205},
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.}
}