Coinduction functor and simple comodules |
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Authors: | L. El Kaoutit J. Gómez-Torrecillas |
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Affiliation: | 1.Departamento de álgebra, Facultad de Educación y Humanidades,Universidad de Granada,Ceuta,Spain;2.Departamento de álgebra, Facultad de Ciencias,Universidad de Granada,Granada,Spain |
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Abstract: | Consider a coring with exact rational functor, and a finitely generated and projective right comodule. We construct a functor (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 group-graded modules is also given. |
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