§ 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 …

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 …

Theorem.—A finitely generated A-module M is projective if and only if the Fitting ideals? V
(M), v^ 0, are of the form Aev where¡?„is an idempotent element of A. In [4, § 4.4, Theorem …

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 …

A where Po is a projective module over A (see [2],[5] and [6]). If A is not normal it is known
that a projective module P over A [X] need not come from A (see for instance [2], p. 325) …

In 5, I provided a method whereby the study of an Artinian module A over a commutative ring
R (throughout the paper, R will denote a commutative ring with identity) can, for some …

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 …

Throughout this note, except in? 3, we adhere to the following notation and conventions: R
denotes a commutative Noetherian ring, an R-algebra is always finitely generated as an R …

We characterize left coherent, left Noetherian, and left Artinian rings by the flatness,
projectivity, and injectivity of the character module of certain left/{-modules. Introduction. The …

Some Theorems about Projective Modules over Polynomial Rings Page 1 JOURNAL OF
ALGEBRA 86, 150-158 (1984) Some Theorems about Projective Modules over Polynomial …