RINGS OVER WHICH FLAT COVERS OF SIMPLE MODULES ARE PROJECTIVE Page 1
Journal of Algebra and Its Applications Vol. 11, No. 3 (2012) 1250046 (7 pages) c© World …

If R is a right coherent ring, then left R-modules have covers by submodules of flat R-
modules if and only if all injective left R-modules have flat covers. This is the case if R is …

In Bican et al., it is proved that all modules over an arbitrary ring have flat covers. In this
article, we shall study rings over which flat covers of finitely generated modules are …

In this paper, we investigate the notions of X⊥‐projective, X‐injective, and X‐flat modules
and give some characterizations of these modules, where X is a class of left modules. We …

When every finitely generated flat module is projective Page 1 Journal of Algebra 277 (2004)
542–558 www.elsevier.com/locate/jalgebra When every finitely generated flat module is …

Let $ R $ be a ring and $ M $ be an $ R $-module. In this paper we investigate modules $ M
$ such that every (simple) cosingular $ R $-module is $ M $-projective. We prove that every …

Let R be a ring, na fixed nonnegative integer and In (Fn) the class of all left (right) R-modules
of injective (flat) dimension at most n. A left R-module M (resp., right R-module F) is called n …

We characterize left Noetherian rings in terms of the duality property of injective
preenvelopes and flat precovers. For a left and right Noetherian ring R, we prove that the flat …

THE EXISTENCE OF FLAT COVERS flat, then <j> is called a flat cover of M if F' F —^— MF (b)
¡ \ F —^ M Page 1 proceedings OF THE AMERICAN MATHEMATICAL SOCIETY Volume 122 …

We introduce nets in rings, which turn out to describe right flat modules and left flat modules
over a fixed ring R at the same time. As an application we prove that for a finitely generated …