Relative Faithful Exact Functors and Their Applications to Homological Modules
Commutative Algebra
2026-03-03 v1
Abstract
The notions of faithfully projective, faithfully flat, and faithfully injective modules--defined as modules for which the three classical homological functors are both faithful and exact--play fundamental roles across various areas of algebra. In this paper, we extend these notions to the setting of -operation theory. By introducing the concept of -faithfully exact functors, we define and investigate the notions of -faithfully projective, -faithfully flat, and -faithfully injective modules. We establish their fundamental properties and demonstrate their effectiveness in generalizing classical results.
Keywords
Cite
@article{arxiv.2603.00970,
title = {Relative Faithful Exact Functors and Their Applications to Homological Modules},
author = {Xiaolei Zhang and Lei Qiao and Hwankoo Kim},
journal= {arXiv preprint arXiv:2603.00970},
year = {2026}
}