Download E-books FPF Ring Theory: Faithful Modules and Generators of Mod-R (London Mathematical Society Lecture Note Series) PDF

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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