Commutative Ring Theory

4 Ascending Chain Conditions and Associated Primes

Paul-Jean Cahen Laboratoire de Mathématiques Fondamentales et Appliquées, Case 322, Faculté des Sciences de Saint-Jérôme, Université d’Aix Marseille III, 13 397 Marseille Cedex 13, France

ABSTRACT: It is known that associated and weakly associated primes are the same for a noetherian domain; here it is shown that a.c.c. on divisorial ideals (Mori domains) implies equality of associated and weakly associated primes for A/I, where I is divisorial. Converse implications do not hold and a.c.c. on principal ideals does not imply nor is implied by equality of associated and weakly associated primes for A/I, where I is principal.

Introduction

For classical notions and definitions on rings, we refer ...