Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

Page 1 Modern Birkhäuser Classics Alberto Facchini Module Theory Endomorphism rings and
direct sum decompositions in some classes of modules S. Birkhäuser Page 2 US Birkhäuser …

We answer a question posed by Warfield in 1975: the Krull-Schmidt Theorem does not hold
for serial modules, as we show via an example. Nevertheless we prove a weak form of the …

The main theme in classical ring theory is the structure theory of rings of a particular kind.
For example, no one text book in ring theory could miss the Wedderburn-Artin theorem …

Until now there has been no suitable dimension to measure how far a module deviates from
being uniserial. We define and study a new dimension, which we call uniserial dimension …

We counting valuation dimension of the ring Zn. Recently, Ghorbani and Nazemian
introduced the notion of a valuation dimension of a commutative rings that measures of how …

We apply minimal weakly generating sets to study the existence of Add (UR)-covers for a
uniserial module U R. If UR is a uniserial right module over a ring R, then S:= End (UR) has …

A module M is called lifting if every submodule A of M contains a direct summand B of M
such that Bce,→ A in M. We call M is (strongly) FIlifting if every fully invariant submodule A of …

We construct examples of infinitely generated almost*-moduels, ie of infinitely generated
small modules satisfying the Colpi's condition C (K) for all R< N0. We also prove that the …

We present some methods for calculating the module's uniserial dimension that finitely g
enerated o ver a DVD in this article. The idea of a module's uniserial dimension over a …