… duality property of injective preenvelopes and flat precovers. For … flat dimension of the
injective envelope of any (Gorenstein) flat left R-module is at most the flat dimension of the injective …

… flat covers of modules was introduced by Enochs in [3]. In this paper, we study the relation
between flat covers and injective envelopes … ) mean the flat dimension and injective dimension …

… the ℒ-projective cover of the P(ℒ)-injective envelope of this module. … 3.4.8) that the flat cover
of the cotorsion envelope of M is … As we know, the injective envelope of R R need not always …

… These notions were directly motivated by injective envelopes. In this general setting, all …
envelopes and covers, such as injective envelopes, pure injective envelopes, projective covers …

Let R be a ring, n a fixed non-negative integer and ℱ ℐ n (ℱ n ) the class of all right (left) R-modules
of FP-injective (flat) dimension at most n. We prove that ( is a perfect cotorsion theory …

… C-envelope of M. If C is the class of injective modules, then we get the usual injective envelopes…
For C some familiar class of modules, say the class of flat (respectively finitely projective, …

… an associative ring R with identity admits a flat cover. Enochs, Estrada, Garcia … a flat
cover for any object in a Grothendieck category with a flat generator. The existence of pure-injective …

… flat envelope of a module, if it exists is unique up to isomorphism. If we replace flat by injective
… Let M be a finitely generated right module and f: P – M* the projective cover of its dual …

… of an injective envelope, injective covers can be … an injective cover from the existence of a
precover. Some of the proofs will apply to other types of covers and envelopes (eg, flat covers). …

… to that of an injective envelope is a projective cover. Projective covers are also unique up to
… that the existence of a flat precover implies the existence of a flat cover in the category of left …