On $e^{\ast }$-topological Rings

The main purpose of this paper is to introduce the concept of $e^{\ast }$-topological ring. This class appears as a generalized form of the class of $\beta$-topological rings. In addition, we have discussed the relation between the concept of $e^{\ast }$-topological ring and some other types of topological rings existing in the literature. Also, some fundamental results about $e^{\ast }$-topological rings are revealed. Furthermore, we give some counterexamples related to our results.