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. A left R-module M (resp., right R-module N) is called weak injective (resp.,
weak flat) if (resp.,) for every super finitely presented left R-module F. By replacing finitely …

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 …

In this short paper, the homological functors are used to show that a simple module is flat if
and only if it is injective. It is used to give a characterization of Von Neumann regular ring …

Given modules M and N, M is said to be N-subprojective if for every epimorphism g: B→ N
and homomorphism f: M→ N, there exists a homomorphism h: M→ B such that gh= f. For a …

Let cp be a ring homomorphism from a ring R to a ring Q. If Q is flat as a right R-module and
q is a ring epimorphism, we say that QR is a flat epimorphism. If Q is projective with respect …

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 …

Finitely generated modules with finite F-representation type over Noetherian (local) rings of
prime characteristic p are studied. If a ring R has finite F-representation type or, more …

In this paper we will first establish a duality between in jectivity and flatness for modules.
That is: Let E be a faithfully in jective module". Then, for each module A, we have W, dim. A …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …