We reprove that any injective module has a direct decomposition into a directly finite and a
purely infinite part ([8], Theorem 6), and we show that this decomposition has a strong …

Our concern is with modules M such that every homomorphism from a closed submodule of
M to M can be lifted to M. Although such modules share some of the properties of extending …

We prove two theorems on continuous modules: Decomposition Theorem. A continuous
module M has a decomposition, M= M1⊕ M2, such that M1 is essential over a direct sum of …

We remind the reader that this definition is dual to that of a continuous module (Utumi [6],
Mohamed and Bouhy [4]) which in turn extends that of a (quasi-) injective module, and that it …

Let M be an Λ-module and Jl a subfamily of the family X (M) of all submodules of M. M is said
to have the extending property of modules for< Jl provided that, for any A in< Jly there exists …

A module is said to be extending, if every closed (ie complement) submodule is a direct
summand. This property is usually denoted by (Q). It is, obviously, equivalent to the …

A module is said to be copure injective if it is injective with respect to all modules A⊂ B with
B/A injective. We first characterize submodules that have the extension property with respect …

It is clear that this defintion depends on the direct decomposition of T. We have studied a
cyclic hollow module in [3]. We note that the concept dual to a cyclic hollow module is a …

1. Introduction. The concept of continuous modules owes its origin to Von Neumann's work
on continuous geometries [16], and Utumi's work on continuous rings ([12],[13],[14]). L …

A module is extending (or a CS-module, or a module with if every submodule is essential in
a direct summand (equivalen tly, if every closed submodule is a direct summand). Extending …