Let ℒ be a class of right modules, whenever covers and envelopes exist, we show that if ℒ is
closed under extensions and direct summands, then P (ℒ), the class of all ℒ-projective right …

In this paper we prove that the extension of pure injective module is pure injective if and only
if the cotorsion envelope and the pure injective envelope of any R-module M are isomorphic …

Let R be a ring, X a class of left R‐modules, S the class of submodules of X, and Q the class
of quotient‐modules of X. It is shown that SQ is precovering (preenveloping) if and only if …

Full article: Envelopes and Covers Over Pullback-Pushout Diagrams Skip to Main Content
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We prove the following results for a ring R.(a) If C is a class of right R-modules closed under
direct summands and isomorphisms, then every right R-module has an epic C-envelope if …

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 …

All the rings will be associative with identity and the modules will be unital. If M is a right
module we denote by M* the dual module Hom „(M., R) of M. If M is a right R-module, a flat …

Let R be a commutative ring with identity. Denote by w𝒫 w the class of weak w-projective R-
modules and by w𝒫 w⊥ the right orthogonal complement of w𝒫 w. It is shown that (w𝒫 w …

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 …

Full article: DG-Injective Covers, #-Injective Covers Skip to Main Content Taylor and Francis
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