Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism Y-
> M is neat in Y, ie, the induced map Hom (S, Y)-> Hom (S, M) is surjective for any simple …

Let R be a ring. A right R-module M is said to be neat-flat if the kernel of any epimorphism
Y→ M is neat in Y, ie, the induced map Hom (S, Y)→ Hom (S, M) is surjective for any simple …

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 …

We shall call a ring R a left IF ring if every injective left R-module is flat. The purpose of this
paper is to characterize left and two-sided IF rings in several ways and to give some …

Given modules RM and AR, RM is said to be absolutely AR-pure if A⊗ M→ A⊗ B is a
monomorphism for every extension RB of RM. For a module AR, the absolutely pure domain …

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 …

A submodule N of a right R-module M is called coneat if for every simple right R-module S,
any homomorphism $ N {\rightarrow} S $ can be extended to a homomorphism $ M …

Let $ R $ be a commutative ring and let $ S $ be an $ R $-algebra. It is well-known that if $ N
$ is an injective $ R $-module, then $\operatorname {Hom} _R (S, N) $ is an injective $ S …

Let ℱ 𝒫∞ R be the class of all left R-modules M which has a projective resolution by finitely
generated projectives. An exact sequence 0→ A→ B→ C→ 0 of right R-modules is called …

Abstract A right R-module M is said to be finendo provided that as a left module over its
endomorphism ring it is finitely generated. Let B= End MR. Then B n→ M→ 0 is exact for …