Infinite Comatrix Corings
Rings and Algebras
2007-05-23 v1
Abstract
We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of the notions of comatrix coring and Galois comodule which avoid finiteness conditions. A sufficient condition for a coring to be isomorphic to an infinite comatrix coring is found. We deduce in particular that any coalgebra over a field and the coring associated to a group-graded ring are isomorphic to adequate infinite comatrix corings. We also characterize when the free module canonically associated to a (not necessarily finite) set of group like elements is Galois.
Keywords
Cite
@article{arxiv.math/0403249,
title = {Infinite Comatrix Corings},
author = {L. El Kaoutit and J. Gomez-Torrecillas},
journal= {arXiv preprint arXiv:math/0403249},
year = {2007}
}