Quasi-Frobenius functors. Applications

Details Quasi-Frobenius functors. Applications Quasi-Frobenius functors. Applications

2006-12-21

arxiv.org/abs/math/0612662v2

Mathematics

Rings and Algebras

20 pages, major changes in v2

Scientific paper

We investigate functors between abelian categories having a left adjoint and a right adjoint that are \emph{similar} (these functors are called \emph{quasi-Frobenius functors}). We introduce the notion of a \emph{quasi-Frobenius bimodule} and give a characterization of these bimodules in terms of quasi-Frobenius functors. Some applications to corings and graded rings are presented. In particular, the concept of quasi-Frobenius homomorphism of corings is introduced. Finally, a version of the endomorphism ring Theorem for quasi-Frobenius extensions in terms of corings is obtained.

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