Graded Equivalence for Graded Idempotent Rings
Rings and Algebras
2026-04-15 v1
Abstract
In this paper, we extend the study of graded equivalences to the case of general idempotent graded rings. We prove that the existence of a graded equivalence between two categories of graded torsion-free unital modules may be characterized by the existence of a Morita context with surjective trace maps. As an application of our results we relate certain lattices of graded submodules and graded ideals of graded equivalent garded rings and give some properties invariant under graded equivalences.
Cite
@article{arxiv.2604.12355,
title = {Graded Equivalence for Graded Idempotent Rings},
author = {Mikhailo Dokuchaev and Juan Jacobo Simón},
journal= {arXiv preprint arXiv:2604.12355},
year = {2026}
}