Rough Rings, Rough Subrings, and Rough Ideals
Fakhry Asad Agusfrianto

Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta

Abstract

The basic concept in algebra which is set theory can be expanded into rough sets. Basic operations on the set such as intersection, union, differences, and complements can still apply to rough sets. Furthermore, one of the applications of rough sets is the use of rough matrices in decision-making. Furthermore, researchers of mathematics or informatics who work on rough sets connect the concept of rough sets with algebraic structures (groups, rings, and modules) so that a concept called rough algebraic structures is obtained. Because research related to rough sets is mostly carried out at the same time, different concepts related to rough sets and rough algebraic structures are obtained. In this paper, another definition of the rough ring and rough subring will be given. Furthermore, examples and theorems related to rough rings and rough subrings will be given. Furthermore, based on the definition of the rough ring and rough subring that has been previously defined, the definition of the left ideal and the right ideal of the rough ring will be given. Furthermore, an example will be given regarding rough ideals. Finally, will be shown the rough ideal-related theorem.

Keywords: Rough Sets, Rough Rings, Rough Subrings, Rough Ideals

Topic: Mathematics