ar X iv : m at h / 06 12 66 2 v 2 [ m at h . R A ] 3 S ep 2 00 8 QUASI - FROBENIUS FUNCTORS . APPLICATIONS

We investigate functors between abelian categories having a left adjoint and a right adjoint that are similar (these functors are called quasi-Frobenius functors). We introduce the notion of a 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. 2000 Mathematics Subject Classification: 16W30, 16L60