In the paper [4], the author introduced the notion of m-adic free modules in order to give a
differential characterization of regular local rings. Later, more generally, A. Grothendieck …

Let R be a commutative and noetherian ring. It is known tht if R is local with maximal ideal M
and F is a flat R-module, then the Hausdorff completion F of F with the M-adic topology is flat …

§ 1. Let R be a commutative ring with units and m an ideal of R. Let M be an R-module. For
the simplicity we assume that m has a finite base. We consider the m-adic topology on both …

We assume throughout that R is an associative ring with unity whose modules are left unital;
J (R) is the Jacobson radical of R;~ n is the ring of matrices of order n over the ideal~ of R; …

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 …

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 …

In this paper A is a commutative noetherian ring, a an ideal of A and the A-modules are
given the a-adic topology. It is a general feeling that completeness is a kind of finiteness …

Introduction. Let R be a ring and J its Jacobson radical. In [6], I. Kaplansky proved the useful
theorem that, if R is local, ie R/J is a division ring, then any projective R-module is free. In [4] …

Let R be a commutative ring with identity. The purpose of this paper is to introduce and to
study a new class of modules over R called quasi-primaryful R-modules. This class contains …

We assume familiarity with the definitions and basic properties of linearly compact rings and
modules as contained in [6] or [3, Exercises 14 20, pp. 108-111]. In § 1 we show that every …