… will simply be called flat (respectively finitely projective, projective) envelopes. If
envelopes exist they are unique up to isomorphism. C-(pre)covers can be defined dually. …

… We prove the FCC, as well as existence of torsion-free covers and of cotorsion envelopes
in the sense of Enochs, Warfield and Matlis. We also construct approximations by modules of …

… covers exist in the category of topological spaces. Algebraic closures of fields are envelopes
in the … However R has such an envelope if and only if R has no nonzero nilpotent elements. …

… Let ℒ be a class of right modules, whenever covers and envelopes exist, we show that if ℒ
is closed under extensions and direct summands, then P(ℒ), the class of all ℒ-projective right …

… One of our main problems is the existence of X-envelopes for a given class X. This is highly
… of the existence problem, let us establish some elementary properties. We first note that if M -…

… existence of pure injective envelopes of complexes and we enlarge the class of Gorenstein
projective complexes to get Gorenstein flat complexes and show that this class is a covering …

… existence of preenvelopes or precovers of thar modules, it naturally arises the analogour
questton for envelopes or covers. … considering F-envelopes or 3-covers. It follows from ([ll. Car. …

… In this section we study the existence of envelopes by modules of the class ⊥. We prove that
over any noetherian ring the existence of such envelopes is guaranteed for every module. If …

… We study the existence of covers and envelopes by some special functors on the category
of finitely presented modules. As an application, we characterize some important rings using …

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