COMMUNICATIONS IN ALGEBRA, 21(8), 2697-2713 (1993) O N THE IDEAL STRUCTURE OF RIGHT DISTRIBUTIVE RINGS

In t roduc t ion A right distributive ring, right D-ring for short, is a ring whose lattice of right.ideals is distributive. It is well-known that the class of commutative D-domains coincides with the class of Priifer domains. Noncommutative right D-rings were investigated in a paper of Stephenson [13]. Brungs (51 proved that right D-domains are locally right chain rings. So the class of right chain rings is an interesting class of examples (see [3] and the literature quoted therein). Re-cently two papers by Mazureli and Puczyiowski respectively Mazurek showed that some features for right chain rings can be carried over to right D-rings WI, 191). The purpose of this paper is t o study the structure of right ideals in right D-rings. In $1 we first recall some results from [9]. We introduce the relevant condition (MP). A right D-ring is said to satisfy (MP) if it has a completely prime ideal contained in the Jacobson radical. Some examples of right D-rings satisfying (MP) are given. In 52 we first introduce some notions such as right multiplicative ideals, waists and the right associated completely prime ideal P,(I) of a right multi--This wo~k was partially supported by a grant from Conselho Nacional de Desenvolvi-mento Cientifico e Tecnologico (CNPq, Brazil) and Gesellschaft fiir Mathematik und Daten-verarbeitung (GLID, Germany)