On e*-topological rings

Abstract

The main purpose of this manuscript is to introduce the concept of $e^*$-topological ring. This class appears as a generalised version of the class of $\beta$-topological rings. In addition, we have discussed the relation between the concept of $e^*$-topological ring and some other types of topological rings existing in the literature. Also, some fundamental results about $e^*$-topological rings are revealed. Moreover, we give some counterexamples regarding our results.