Frobenius Extensions of Corings

Details Frobenius Extensions of Corings Frobenius Extensions of Corings

2006-12-16

arxiv.org/abs/math/0612477v1

Mathematics

Quantum Algebra

21p. to appear, Communications in Algebra

Scientific paper

Let $\Cc$ and $\Dd$ be two corings over a ring $A$ and $\Cc\stackrel{\lambda}{\longrightarrow}\Dd$ be a morphism of corings. We investigate the situation when the associated induced ("corestriction of scalars") functor $\Mm^\Cc\longrightarrow \Mm^\Dd$ is a Frobenius functor, and call these morphisms Frobenius extensions of corings. The characterization theorem generalizes notions such as Frobenius corings and is applied to several situations; in particular, provided some (general enough) flatness conditions hold, the notion proves to be dual to that of Frobenius extensions of rings (algebras). Several finiteness theorems are given for each case we consider; these theorems extend existing results from Frobenius extensions of rings or from Frobenius corings, showing that a certain finiteness property almost always occur for many instances of Frobenius functors.

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