… introduce a theory of complexes of modules using elementary tools with … envelopes and
covers in this category with respect to some well-established and important classes of complexes…

… of A-covers and B-envelopes of special complexes. We prove … -modules that is bounded
above has an A-cover and each complex of R-modules that is bounded below has a B-envelope …

… of R-modules has a Gorenstein injective cover [Citation9, … of R-modules has a #-Gorenstein
injective cover. These facts … covers of R-modules and -covers of complexes of R-modules…

… In this chapter we define envelopes and covers for a given class of modules … module has
a flat cover, we first prove that every module over an integral domain has a torsion free covering…

… Given an R-module C and a class of R-modules D over a commutative ring R, we … D-envelopes
(respectively, D-covers) and the existence of Hom(C, D)-envelopes or C ⊗D-envelopes (…

… envelope. When F is some class such as the class of flat modules in the category of left R-modules,
an F-cover … In the category of complexes of left R-modules over any ring R the class Ɛ …

… for complexes of modules and their … 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 …

… covers and cotorsion envelopes for any complex of modules. Thus, throughout this section
denotes class of ffat complexes … and is called the class of all cotorsion complexes. Given any …

… complexes may fail to have the same cohomology groups. In this article we will show that
every O-module has a flat precover, and in fact that it has a flat cover (… flat cover of an O-module …

… Covers and envelopes over any class of modules were defined by Enochs in [4] which
unified all the well known covers and envelopes, such as injective envelopes, projective covers …