Coinduction functor and simple comodules
Rings and Algebras
2009-02-13 v1 Group Theory
Abstract
Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (\emph{coinduction functor}) which is right adjoint to the hom-functor represented by this comodule. Using the coinduction functor, we establish a bijective map between the set of representative classes of torsion simple right comodules and the set of representative classes of simple right modules over the endomorphism ring. A detailed application to a group-graded modules is also given.
Cite
@article{arxiv.0902.2116,
title = {Coinduction functor and simple comodules},
author = {L. El Kaoutit and J. Gómez-Torrecillas},
journal= {arXiv preprint arXiv:0902.2116},
year = {2009}
}