When are the d-ideals of a C(X) closed under addition?
by
Melvin Henriksen
Harvey Mudd College

Throughout A will denote a semiprime f-ring. A ring ideal I of A that contains the annihilator of the annihilator of each of its elements is called a d-ideal. Such ideal have been studied by many authors including Bernau, Bigard, Keimel, and Wolfenstein, Artico, Marconi, and Moresco, Huijsmans and dePagter, Henriksen and Kopperman, S. Larson, and most recently Azarpaneh, Karamzadeh, and Rezai Aliabad. Different names are used for this concept because many were unaware of the work of others. The question of the title was proposed by the last set of authors. The literature in this area is surveyed, and partial answers to this question are given; e.g., the answer is yes if X is an almost P-space or an F-space, and X has this property iff \betaX does. Help may be solicited from the audience.

Date received: February 10, 2000