Research Communication | Open Access
Volume 2020 | Communication ID 88 |

On the topology in zero-dimensional subrings of a product of rings

Hassan Mouadi, Driss Karim
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.