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 …

The main theorem of the paper" Flatness and Injectivity of Simple Modules over a
Commutative Ring" by Xu Jinzhong which appeared in Communications in Algebra 19 (2) …

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 …

It is proved that a module M over a commutative noetherian ring R is injective if Ext _ R^ i
((R/\mathfrak p) _\mathfrak p, M)= 0 Ext R i ((R/p) p, M)= 0 holds for every i\geqslant 1 i⩾ 1 …

Projectivity and flatness over the endomorphism ring of a finitely generated module Page 1
IJMMS 2004:30, 1581–1588 PII. S0161171204310082 http://ijmms.hindawi.com © Hindawi …

In this work all rings are associative with unit unless otherwise stated, and all modules are
unital. If M is a left R-module, a flat preenvelope of M is a homomorphism M–“F, with F flat …

The aim of this paper is to study a property of a special kind of exact functors and give some
applications to projective modules and injective modules. In section 1 we introduce the …

Publisher Summary This chapter describes the quasi-simple modules and weak transitivity.
If RVD be an R, D-bimodule, where D is a division ring R is a ring and RV is a uniform …

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 …

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 …