Affiliation:
1. Faculty of sciences and technologies, University Hassan of Casablanca, Tarik Bnou Ziad Street, Hospitals, Casablanca, Morocco
Abstract
Let R be a ring and {Ri}i?I a family of zero-dimensional rings. We define the
Zariski topology on Z(R,?Ri) and study their basic properties. Moreover,
we define a topology on Z(R,?Ri) by using ultrafilters; it is called the
ultrafilter topology and we demonstrate that this topology is finer than the
Zariski topology. We show that the ultrafilter limit point of a collections
of subrings of Z(R,?Ri) is a zero-dimensional ring. Its relationship with
F-lim and the direct limit of a family of rings are studied.
Publisher
National Library of Serbia