Precovers and preenvelopes were introduced in the early eighties by Enochs [48] and,
independently, by Auslander and Smalø [16]. Enochs gave a general definition in terms of …

After the introduction hy Enochs [9] of the concepts of (pre) erlveIope and I llrejcover of a
module 1r1 a gi\wi class F of modules, there has been great interest in tllelr stud;, specially …

In this paper we give two different proofs that the flat cover conjecture is true: that is, every
module has a flat cover. The two proofs are of completely different nature, and, we hope, will …

The purpose of this study is to give an up-to-date presentation of known and new results on
extending modules and related notions with respect to an R-module class X. By assuming …

A well known problem in the theory of envelopes is to characterize those rings having the
property that every (finitely generated, finitely presented, simple) module has a projective …

A module is extending (or CS, C1) if every complement submodule is a direct summand or,
equivalently, every submodule is essential in a direct summand. The terms extending and …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …

According to classic results of Matlis [lo, Theorem 2.5, 2.71 every injective module over a
Noetherian ring A can be expressed uniquely as the direct sum of indecomposable injective …

Over the last few years, the study of complexes has become increasingly important. To date,
however, most of the research is scattered throughout the literature or available only as …

The restricted injective envelopes with respect to various types of preradicals have been
studied by many authors (see eg [2],[6],[8],[10]). In the second paragraph we shall dualize …