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 …

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 …

Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective
hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R …

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 prove that for a ring $ R $, the following are equivalent:(i) Every right $ R $-module is a
direct sum of extending modules, and (ii) $ R $ has finite type and right colocal type (ie …

A theorem of Cartan-Eilenberg (Cartan, H., Eilenberg, S.(1956). Homological Algebra.
Princeton: Princeton University Press, pp. 390.) states that a ring R is right Noetherian iff …

A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …

It is known that every complex of left R-modules has an exact cover. We consider the
question of finding R for which every complex of left i?-modules has an exact envelope. We …

Full article: Coherent rings and absolutely pure covers Skip to Main Content Taylor and Francis
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A submodule N of a module M is called S-closed (in M) if M/N is nonsingular. It is well-known
that the class Closed of short exact sequences determined by closed submodules is a …