University of Guilan Journal of Algebra and Related Topics 2345-3931 9 1 2021 06 01 On beta-topological rings 51 60 4808 10.22124/jart.2021.14595.1167 EN S. Billawria Department of Mathematics, University of Jammu, Jammu, India. Sh. Sharma Deptarment of Mathematics , University of Jammu, Jammu, India Journal Article 2019 10 01 In this paper, we introduce a generalized form of the class of topological<br /> rings, namely -topological rings by using -open sets which itself is a generalized form<br /> of open sets. Translation of open(closed) sets and multiplication by invertible elements<br /> of open(closed) sets of the -topological rings are investigated. Some other useful results<br /> on -topological rings are also given. Examples of -topological rings which fails to be<br /> topological rings are also provided. We further de ne -topological rings with unity in the<br /> sequel and presented some results on it. beta -open sets beta -closed sets beta-topological ring beta -continuous mappings https://jart.guilan.ac.ir/article_4808_f795e37ed6a719ddea9b9e2a264ac7ae.pdf