Graded Equivalence for Graded Idempotent Rings

TL;DR

This paper extends the theory of graded equivalences to general idempotent graded rings, characterizing them via Morita contexts and exploring invariants of graded submodules and ideals.

Contribution

It introduces a new characterization of graded equivalences using Morita contexts with surjective trace maps for idempotent graded rings.

Findings

Graded equivalence characterized by Morita contexts with surjective trace maps.

Relations between lattices of graded submodules and ideals under graded equivalences.

Identification of properties invariant under graded equivalences.

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.