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

2015/03/26 by Pedro A. Guil Asensio, Asensio, Pedro A. Guil, Serap Sahinkaya +3
Mathematics · #16D40 #16D80 #16L60 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16D40 #msc:16D80 #msc:16L60

paper · pdf · doi:10.48550/arxiv.1503.07815

To appear in Israel Journal of Mathematics

arxiv created 2015/03/26 · arxiv updated 2015/03/27

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 set-theoretic counting arguments initiated by Osofsky. Several corollaries and examples to illustrate their applications are given.

Related

• FP-injective and weakly quasi-Frobenius rings
• Pseudo-Frobenius graded algebras with enough idempotents
• Quasi-co-Frobenius corings as Galois comodules
• Frobenius methods in combinatorics
• Formal matrix representations of pseudo-Frobenius and Frobenius rings