%0 Journal Article
%A Ibrahim, H.
%A Khalaf, A.
%T Topological Rings and Modules Via Operations
%J Iranian Journal of Mathematical Sciences and Informatics
%V 16
%N 2
%U http://ijmsi.ir/article-1-1208-en.html
%R 10.52547/ijmsi.16.2.31
%D 2021
%K Operations, $alpha_{beta}$-Open set, Rins, $alpha_{(beta, beta)}$-Topological rings, $alpha_{(beta, gamma)}$-Topological $R$-modules,
%X The structure of an $alpha_{(beta, beta)}$-topological ring is richer in comparison with the structure of an $alpha_{(beta, beta)}$-topological group. The theory of $alpha_{(beta, beta)}$-topological rings has many common features with the theory of $alpha_{(beta, beta)}$-topological groups. Formally, the theory of $alpha_{(beta, beta)}$-topological abelian groups is included in the theory of $alpha_{(beta, beta)}$-topological rings. The purpose of this paper is to introduce and study the concepts of $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-topological $R$-modules. we show how they may be introduced by specifying the neighborhoods of zero, and present some basic constructions. We provide fundamental concepts and basic results on $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-topological $R$-modules.
%> http://ijmsi.ir/article-1-1208-en.pdf
%P 31-48
%& 31
%!
%9 Research paper
%L A-10-3090-1
%+ Department of Mathematics, Faculty of Education, University of Zakho
%G eng
%@ 1735-4463
%[ 2021