THE TOPOLOGY ON THE PRODUCT OF QUASI-LOCAL RINGS

Abstract

Let $\{R_i\}_{i\in I}$ be a family of quasi-local rings, and let $R=\prod_{i\in I}R_i$ be their product. In this paper, we investigate the prime spectrum of $R$ under different topologies, with special attention given to maximal ideals based on the ultrafilters of $I$. Additionally, we will compute the number of topologies on $R$.