Quasi-co-Frobenius corings as Galois comodules

TL;DR

This paper explores quasi-Frobenius properties of corings, offering new characterizations and linking them to Galois comodules with firm coinvariant rings, advancing the understanding of their structure.

Contribution

It introduces novel characterizations of quasi-Frobenius corings and connects these properties to Galois comodules with a firm coinvariant ring.

Findings

Characterization of locally quasi-Frobenius corings as locally projective generators

New equivalences for quasi-Frobenius-type properties of corings

Application of Galois comodules theory to coring properties

Abstract

We compare several quasi-Frobenius-type properties for corings that appeared recently in literature and provide several new characterizations for each of these properties. By applying the theory of Galois comodules with a firm coinvariant ring, we can characterize a locally quasi-Frobenius (quasi-co-Frobenius) coring as a locally projective generator in its category of comodules.