This is the first book on the subject of FPF rings and the systematic use of the notion of the
generator of the category mod-R of all right R-modules and its relationship to faithful …

INTRODUCTION In the broadest sense, this is a study of commutative rings which satisfy the
(finitely) pseudo-Frobenius (or (F) PF) condition: All (finitely generated) faithful modules …

An R-module G over a ring R is a generator in the category mod-R of all right R-modules if
every right R-module M is an epimorphic image of a direct sum of copies of G. This happens …

Lntroduction It is easily seen that if an R-module is a generator in the category mod-R, then it
is faithful. However, the converse is not necessarily true. Naturally one is led to ask for which …

A ring R is right FPF if eacn finitely generated faithful right R module is a generator of MOP-
R, the category of right R modules. Dedekind domains are FPF as well as quasi-Frobenius …

1* Introduction* An associative ring R is called a left (F) PF ring if every (finitely generated)
faithful module generates the category of left ϋ?-modules. Azumaya [1], Osofsky [7], and …

The class of quasi-Frobenius rings (short: QF rings) is one of the most interesting classes of
non-semisimple rings. Since RM Thrall [53] introduced QF-1, QF-2 and QF-3 rings as its …

First published in 1982. These lectures are in two parts. Part I, entitled injective Modules
Over Levitzki Rings, studies an injective module E and chain conditions on the set A^(E, R) …

(right) PF-rings. This class of rings and another related generalization of quasi-Frobenius
rings, the (two-sided) cogenerator rings, have been studied recently by a number of authors …

A ring R is right finitely pseudo Frobenius (FPF) if every finitely generated faithful right jR-
module generates the category of right jR-modules. In [2], C. Faith has shown that a …