This can be the 1st publication almost about FPF earrings and the systematic use of the idea of the generator of the class mod-R of o.k. R-modules and its courting to trustworthy modules. This includes 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. beaches, R. and S. Wiegand and P. Vamos, between others. FPF jewelry contain quasi-Frobenius earrings (and hence finite jewelry over fields), pseudo-Frobenius (PF) jewelry (and hence injective cogenerator rings), bounded Dedekind top earrings and the next commutative jewelry; self-injective earrings, Prufer jewelry, all jewelry over which each finitely generated module decomposes right into a direct sum of cyclic modules (=FGC rings), and consequently virtually maximal valuation earrings. Any product (finite or countless) of commutative or self-basic PFP earrings is FPF. a few vital sessions of FPF jewelry are thoroughly characterized together with semiprime Neotherian, semiperfect Neotherian, ideal nonsingular major, normal and self-injective earrings. Finite workforce jewelry over PF or commutative injective earrings are FPF. This paintings is the fruits of a decade of study and writing by means of the authors and comprises all identified theorems almost about noncommutative FPF earrings. This e-book might be of curiosity to specialist mathematicians, particularly people with an curiosity in noncommutative ring idea and module concept.
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