Some results of topological rings

Abstract

In this paper, we introduced several results of the topological ring. We proved that if N is a norm on the ring R, then any topology with matric space d which is defined by N is a topological ring. Also, if G is a topological group and N ≤ G, so the closure of N is also subgroup of G. Finally, we study the relation between image of f and the quotient of R\\Ker (f). We showed that the ideal concept is very important to understand the ring in this study. Also, we applied this concept by new way which is topological ideal over the topological ring.