Ring theory | Module theory

Quasi-Frobenius ring

In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps the most important generalization is that of quasi-Frobenius rings (QF rings), which are in turn generalized by right pseudo-Frobenius rings (PF rings) and right finitely pseudo-Frobenius rings (FPF rings). Other diverse generalizations of quasi-Frobenius rings include QF-1, QF-2 and QF-3 rings. These types of rings can be viewed as descendants of algebras examined by Georg Frobenius. A partial list of pioneers in quasi-Frobenius rings includes R. Brauer, K. Morita, T. Nakayama, C. J. Nesbitt, and R. M. Thrall. (Wikipedia).

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Related pages

Quotient ring | Injective module | Kasch ring | Gorenstein ring | Injective hull | Artinian ring | Jacobson radical | Free module | Projective module | Minimal ideal | Quasi-Frobenius Lie algebra | Socle (mathematics) | Noetherian ring | Ring theory | Morita equivalence | Serial module | Local ring | Balanced module | Frobenius algebra | Generator (category theory) | Finitely generated module | Injective cogenerator