The structure of corings: Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties

Details The structure of corings: Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties The structure of corings: Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties

2000-02-14

arxiv.org/abs/math/0002105v2

Mathematics

Rings and Algebras

22 pages, AMS-LaTeX, uses amscd. More examples of corings and references added

Scientific paper

Given a ring $A$ and an $A$-coring $\cC$ we study when the forgetful functor from the category of right $\cC$-comodules to the category of right $A$-modules and its right adjoint $-\otimes_A\cC$ are separable. We then proceed to study when the induction functor $-\otimes_A\cC$ is also the left adjoint of the forgetful functor. This question is closely related to the problem when $A\to {}_A{\rm Hom}(\cC,A)$ is a Frobenius extension. We introduce the notion of a Galois coring and analyse when the tensor functor over the subring of $A$ fixed under the coaction of $\cC$ is an equivalence. We also comment on possible dualisation of the notion of a coring.

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