… Dually, we have the definitions of a 𝒞-(pre)envelope. 𝒞-… perfect cotorsion pair, and so all
modules over a right coherent ring have Gorenstein flat covers. We will extend this result to the …

… of the class of flat modules is called the class of cotorsion modules [3… that the kernel of a flat
cover is cotorsion. It seems to be a … Since λ is a cotorsion envelope, it is also a twist envelope. …

… -envelopes. In addition, a necessary and sufficient condition is given so that every module
has an epimorphic FPn-Flat-envelope… We begin by checking that we have a cotorsion pair. Let …

… flat covers and V -Gorenstein flat preenvelopes for any left R-module. Also we prove that (V
-GF, V -GF⊥ ) is a perfect hereditary cotorsion … -module has an F -cover and a C-envelope. A …

… envelopes for modules over any ring yields minimal injective resolutions; dually, in settings
where projective covers … fact and extend it to the case of complexes of flat cotorsion modules. …

… @0Þ of the cotorsion envelope of RR is cotorsion. If CR is a flat S-cotorsion module, then CR
… This will enable us to characterize the flat cover of a simple module over a semiperfect ring. …

… the first half of a so-called perfect cotorsion pair as introduced by Salce; this is stronger than
being covering. … But flat envelopes of left-modules do not necessarily exist, see [9, thm. 6.1]. …

… That characterization was very useful in proving the existence of flat covers for … of flat
covers gave the existence of cotorsion envelopes. However, no characterization of cotorsion …

… these classes will form part of what is called a cotorsion theory. When this holds we will
frequently have certain envelopes and covers. A cotorsion theory is defined as a pair ( …

… As a consequence, we show that if ℱ = 𝒢 ⊥ for some class 𝒢 of R-modules, then is a
cotorsion pair, but may not be a cotorsion pair in general. If, furthermore, 𝒢 is a Kaplansky class …