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 well-known that if R is a Noetherian ring or a local ring, then every finitely generated flat
R-module is projective (cf.(1),(3), R need not be commutative.). It is also known that if R is a …

The flat dimensions of injective modules Page 1 manuscripta math. 78, 165- 177 (1993)
manuscripta mathematica Spfinger-Verlag 1~3 THE FLAT DIMENSIONS OF INJECTIVE …

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 …

868 MARTINEZ HERNANDEZ where F'is a flat and F-divisible module, can be completed
commutatively. b) The diagram can be completed only by means of autornorphisms of F. In …

Throughout this paper all rings considered will be commutative rings with identity. We shall
consider the consequences for a ring of the flatness of certain classes of its modules. Since …

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 …

The injective hull of a module M can be characterized as a homomorphism f: M~ E (with E an
injective module) such that for each homomorphism g: M--* E'with E'injective, there exists a …

In this note we shall consider rings A with the property that any flat and finitely generated A-
module is projective, and we will prove that this class of rings is rather big. If we require that …

Introduction. Let R be an integral domain with quotient field Q, and let A be a module over R.
A is said to be a divisible R-module, if rA= A for every r7OER. An element xEA is said to be a …