ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 54 and 13 Karamzadeh, O. A. S., University of Chamran, Iran Some Algebraic Aspects of C(X) Some Algebraic Aspects of C(X) It is shown that X is an extremally disconnected space if and only if C(X) is a Baer ring. We also give several new algebraic characterizations of basically disconnected spaces. These characterizations are then used to give a unified proof of the facts that X is extremally (basically) disconnected if and only if βX is extremally (basically) disconnected space. Zero-dimensional and strongly zero-dimensional spaces are also characterized similarly. It is shown that X is a strongly zero-dimensional F-space if and only if each minimal prime ideal in C(X) is generated by idempotents.