On beta-topological rings

In this paper, we introduce a generalized form of the class of topological rings, namely -topological rings by using -open sets which itself is a generalized form of open sets. Translation of open(closed) sets and multiplication by invertible elements of open(closed) sets of the -topological rings are investigated. Some other useful results on -topological rings are also given. Examples of -topological rings which fails to be topological rings are also provided. We further dene -topological rings with unity in the sequel and presented some results on it.