There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

Let R denote a commutative ring with identity. If there exists a chain ${P_0}\subset
{P_1}\subset\cdots\subset {P_n} $ of $ n+ 1$ prime ideals of R, where ${P_n}\ne R $, but no …

A new and more elementary proof is given for LØnsted's theorem that vector bundles over a
finite complex can be represented by projective modules over a noetherian ring. The rings …

Théorie de la dimension dans les anneaux de polynômes Page 1 MÉMORIAL DES
SCIENCES MATHÉMATIQUES PAUL JAFFARD Théorie de la dimension dans les anneaux …

Let R be a commutative ring with identity. R is said to have dimension n, written dim R= n, if
there exists a chain P 0⊂ P 1⊂⋯⊂ P n of n+ 1 prime ideals of R, where P n⊂ R, but no …

IDEAL THEORY IN PULLBACKS Page 1 Chapter 9 IDEAL THEORY IN PULLBACKS
Stefania Gabelli Dipartimento di Matematica Uniuersita degli Studi Roma Pre Largo San L …

Let Q be a prime ideal of R [X 1,..., X n] and let P= Q∩ R. This paper investigates the
relationship between the ranks of Q and P [X 1,..., X n]. The results are used to recover some …

Let R be a commutative ring containing a regular element and let T be the total quotient ring
of R. If F is an invertible ideal of R, then F has a finite basis; this result was originally proved …

These notes are concerned with a number of open problems, the catenary chain
conjectures, some of which are of quite long-standing. In the hope of attracting some new …

Several applications are given of the technique of proving theorems in char 0 (as well as
char/?) by, in some sense," reducing" to char/? and then applying the Frobenius. A" …