This is often the 1st publication with regards to FPF jewelry and the systematic use of the proposal of the generator of the class mod-R of very well R-modules and its dating to devoted modules. This contains out this system, specific of inherent, within the paintings of G Azumaya, H. Bass, R. Dedekind, S. Endo, I. Kaplansky, okay. Morita, T. Nakayama, R. Thrall, and extra lately, W. Brandal, R. Pierce, T. shorelines, R. and S. Wiegand and P. Vamos, between others. FPF earrings comprise quasi-Frobenius jewelry (and therefore finite earrings over fields), pseudo-Frobenius (PF) jewelry (and therefore injective cogenerator rings), bounded Dedekind leading jewelry and the subsequent commutative jewelry; self-injective jewelry, Prufer earrings, all earrings over which each finitely generated module decomposes right into a direct sum of cyclic modules (=FGC rings), and accordingly virtually maximal valuation jewelry. Any product (finite or countless) of commutative or self-basic PFP jewelry is FPF. a few vital sessions of FPF earrings are thoroughly characterized together with semiprime Neotherian, semiperfect Neotherian, ideal nonsingular top, normal and self-injective earrings. Finite workforce jewelry over PF or commutative injective jewelry are FPF. This paintings is the fruits of a decade of study and writing via the authors and contains all identified theorems as regards to noncommutative FPF earrings. This ebook could be of curiosity to expert mathematicians, particularly people with an curiosity in noncommutative ring conception and module idea.
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