Comatrix corings: Galois corings, Descent Theory, and a Structure Theorem for Cosemisimple corings

摘要

In order to extrincate the structure of corings with a finitely generated andprojective generator we give the notion of a comatrix coring. As consequenceswe give generalizations of the main characterizations of faithfully flat Galoiscorings and extensions which work for corings without grouplike elements, aswell as a generalization of the Descent Theorem. We provide also a completedescription of all cosemisimple corings. No restrictions are made over theground noncommutative ring.