Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
16 January 2020 |
31 January 2020 |
10 March 2020 |
Abstract: Let $R$ be a ring and $\{R_{i}\}_{i\in I}$ a family of zero-dimensional rings. In this work, we define the the Zariski topology on $\mathcal{Z}(R,\prod R_{i})$ and study their basic properties. Moreover, we define a topology on $\mathcal{Z}(R,\prod R_{i})$ by using ultrafilters it's called the ultrafilter topology and we demonstrate that this topology is finer than the Zariski topology.