We have studied the Hiking property on a direct sum of completely indecomposable and
cyclic hollow modules over a ring R in [8]. In this note, we shall define the lifting property of …

First we take a right artinian ring R. Then every injective. R-module E is a direct sum of
indecomposable modules. Further for every simple submodule S of Ey there exists a direct …

Following E. Mares [12] and H. Bass [2] we shall first consider a semiperfect module P over a
ring R. One of the important properties of P is the lifting property as follows: Let ί>//(P)= Σ …

MODULES WITH PERFECT DECOMPOSITIONS Page 1 MATH. SCAND. 98 (2006), 19^)3
MODULES WITH PERFECT DECOMPOSITIONS LIDIA ANGELERIHUGEL and MANUEL …

In 1-4] Nakayama proved that every module M over a generalized uniserial ring has a
decomposition M=~) M~ in which each term is A uniserial (ie, its submodules form a chain) …

Throughout R will represent a ring with unit element 1, and all modules will be unitary 7?-
modules. We call a module M a completely indecomposable module if the endomorphism …

It was shown in [5] that a finitely presented pure-injective module M has an indecomposable
decomposition if and only if M is completely pure-injective, that is, every pure quotient of M is …

A module M over a ring R is called a lifting module if every submodule A of M contains a
direct summand K of M such that A/K is a small submodule of M/K (eg, local modules are …

It is proved that a commutative ring with $1 $ has the property that every finitely presented
module is a summand of a direct sum of cyclic modules if and only if it is locally a …

Introduction In this discussion every module over a ring R will be understood to be a left i2-
module. R will always have a unit, and every module will be unitary. The aim of this paper is …