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Mathematics > Rings and Algebras

arXiv:math/0002105 (math)
[Submitted on 14 Feb 2000 (v1), last revised 2 Mar 2000 (this version, v2)]

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

Authors:Tomasz Brzezinski (University of Wales Swansea)
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Abstract: 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.
Comments: 22 pages, AMS-LaTeX, uses amscd. More examples of corings and references added
Subjects: Rings and Algebras (math.RA); Quantum Algebra (math.QA)
Cite as: arXiv:math/0002105 [math.RA]
  (or arXiv:math/0002105v2 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.math/0002105

Submission history

From: Tomasz Brzezinski [view email]
[v1] Mon, 14 Feb 2000 11:00:53 UTC (18 KB)
[v2] Thu, 2 Mar 2000 10:23:00 UTC (19 KB)
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