Abstract
We provide new characterizations of pseudo-Frobenius and quasi-Frobenius rings in terms of tight modules. In the process, we also provide fresh perspectives on FGF and CF conjectures. In particular, we propose new natural extensions of these conjectures which connect them with the classical theory of PF rings. Our techniques are mainly based on settheoretic counting arguments initiated by Osofsky. Several corollaries and examples to illustrate their applications are given.
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Dedicated to Alberto Facchini on his 60th birthday
The first author has been partially supported by the DGI (MTM2010-20940-C02-02) and by the Excellence Research Groups Program of the Séneca Foundation of the Region of Murcia. Part of the sources of both institutions come from the FEDER funds of the European Union.
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Guil Asensio, P.A., Sahinkaya, S. & Srivastava, A.K. New characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture. Isr. J. Math. 214, 121–148 (2016). https://doi.org/10.1007/s11856-016-1351-4
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DOI: https://doi.org/10.1007/s11856-016-1351-4