Quasi-Frobenius Functors. Applications |
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Authors: | F. Castaño Iglesias C. Nǎstǎsescu |
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Affiliation: | 1. Departamento de Estadística y Matemática Aplicada , Universidad de Almería , Almería, Spain;2. Facultatea de Matematic?, Str. Academiei 14 , Bucharest, Romania |
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Abstract: | 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. |
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Keywords: | Coring Graded ring Quasi-Frobenius extension Similar functors |
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