New characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture

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 o...

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Bibliographic Details
Published in:Israel journal of mathematics 2016-07, Vol.214 (1), p.121-148
Main Authors: Guil Asensio, Pedro A., Sahinkaya, Serap, Srivastava, Ashish K.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Modules
Theoretical
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Summary: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.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1351-4