Coinduction functor and simple comodules

Details Coinduction functor and simple comodules Coinduction functor and simple comodules

2009-02-12

arxiv.org/abs/0902.2116v1

Mathematics

Rings and Algebras

Scientific paper

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.

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