Corings with decomposition and semiperfect corings

TL;DR

This paper characterizes corings that decompose into finitely generated left comodules using Galois comatrix corings and shows the associated rational functor is exact, focusing on right semiperfect, locally projective corings.

Contribution

It provides a new characterization of decomposable corings via Galois comatrix corings and analyzes the exactness of the rational functor in this context.

Findings

Corings decompose as direct sums of finitely generated comodules under certain conditions.

The associated rational functor is exact for specific semiperfect corings.

Identification of conditions for Galois comodule projectivity and radical properties.

Abstract

We give a characterization, in terms of Galois infinite comatrix corings, of the corings that decompose as a direct sum of left comodules which are finitely generated as left modules. Then we show that the associated rational functor is exact. This is the case of a right semiperfect coring which is locally projective and whose Galois comodule is a projective left unital module with superfluous radical.