… proofs that the flat cover conjecture is true: that is, every module has a flat cover. The two
proofs … Since the existence of flat precovers implies the existence of flat covers (see [9]), we can …

… We also consider t class of weakly Gorenstein flat modules (see 3 for the definition) and
obtain a relative version of the "flat cover conjecture". Throughout this paper, R will denote …

… In order to provide the first class of rings (Prüfer domains) over which every module has a
flat cover, in this chapter we prove the existence of torsion free coverings over any integral …

… with F flat and ker(cp) cotorsion, then it is a flat precover of M. We also know that a module
M has a flat cover if it has a flat precover [4, Theorem 3.1]. We discuss flat covers of modules in …

… we prove the existence of a flat cover and a … existence of a flat cover for any quasi-coherent
sheaf over the projective line . Some results guaranteeing the existence of general ℱ-covers …

… the existence of a cover (or … the existence of a precover implies the existence of a cover. In
this section we sketch a proof that the existence of a flat precover implies the existence of a flat …

… Since we will prove the existence of flat covers and cotorsion envelopes making use of the
techniques developed by Eklof and Trlifaj (see [4]) over cotorsion theories, we introduce some …

… of torsion-free covers. In [8] these were shown to exist for some modules over commutative
noetherian rings, but the existence of flat covers in general is still an open question. Perhaps …

… Second, for Zn-persistence modules with n > 1, a complete discrete invariant does not exist
as pointed out in [7]—not even if we restrict to finitely generated persistence modules. Thus, …

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