… 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 …

… of any Gorenstein injective left R-module is Gorenstein flat, the class of Gorenstein injective
left … In the proof of the result about the existence of the Gorenstein injective covers we will use …

… [3]) and that of FP∞-injective modules (ie, the absolute … -envelopes. In addition, a
necessary and sufficient condition is given so that every module has an epimorphic FPn-Flat-envelope. …

… of pure injective envelopes of complexes … Gorenstein projective complexes to get Gorenstein
flat complexes and show that this class is a covering class over a commutative Gorenstein …

… Gorenstein flat covers over two sided noetherian rings. And we prove the existence of special
Gorenstein … In this paper, we also consider covers and envelopes in Ch(R), the category of …

… € F, X→ Y is an F-envelope. In fact this proceedure was developed to prove the existence of
Gorenstein injective envelopes over Iwanaga-Gorenstein rings (see Theorem 6.1 of [29] and …

… M+ is Gorenstein flat. Then we consider the existence of Gorenstein injective envelopes for
… character modules of Gorenstein injectives are Gorenstein flat, then every complex has a …

… the class of Gorenstein injective modules is both covering and … modules of Gorenstein
injective modules are Gorenstein flat. … G+ is Gorenstein flat whenever RG is Gorenstein injective. …

… contributing to Gorenstein (pre)covers and (pre)envelopes. … Finally we deal with the existence
of pure injective Gorenstein injective … of Gorenstein injective R-modules are Gorenstein flat. …

… the well known existing envelopes and covers. In particular, … , the investigation of covers
and envelopes will be of interest, … pure injective module M has a Gorenstein flat cover which is …