… and cotorsion theories of modules as developed by Enochs and Salce. In Chapter 2, we prove
that complete cotorsion … of torsion-free covers and of cotorsion envelopes in the sense of …

… In order to prove the existence of these flat covers we will first prove their existence … flat cover
of an O-module in the category of O-premodules is in fact an O-module and so is a flat cover …

… cotorsion envelopes. For this argument we need the fact that there is a single flat module
G which is a test module for cotorsion, ie such that C is cotorsion if and only if Ext I (G, C) = 0. …

… of a module is isomorphic to the ℒ-projective cover of the P(ℒ)-injective envelope of this …
flat cover of the cotorsion envelope of M is isomorphic to the cotorsion envelope of the flat cover …

… R-modules have fiat covers. In this Chapter we also introduce cotorsion modules and explore
the relation between the existence of flat covers and the existence of cotorsion envelopes. …

… property if and only if R is a right cotorsion ring with J(R) right T-… if every cotorsion right
R-module has a flat cover with the … → C(M) will denote a flat cover and a cotorsion envelope of M, …

… on the study of envelopes and covers in this category with … The use of covers and envelopes
in this work is fundamental … existence of covers with respect to some class in case there …

… of flat covers and cotorsion envelopes over a right coherent ring of finite weak global
dimension. Cotorsion … The consistency of the existence of flat covers and cotorsion envelopes is …

… existence of a flat cover and a cotorsion envelope for any quasi-… the existence of ℱ-covers
and ℱ ⊥ -envelopes in the general setting … Covers and envelopes in Grothendieck categories. …

… that of indecomposable direct summands of the cotorsion envelope of R. Actually, we show
that these indecomposable direct summands are just the flat covers of those simple modules. …