DOI: https://doi.org/10.14710/jfma.v8i1.23564

Construction of the Rough Quotient Modules over the Rough Ring by Using Coset Concepts

Aira Rahma  -  Universitas Lampung, Indonesia
*Fitriani Fitriani orcid scopus publons  -  Dept. of Mathematics, Universitas Lampung, Indonesia
Ahmad Faisol orcid scopus  -  Universitas Lampung, Indonesia

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Abstract
Given an ordered pair $(U, \theta)$ where $U$ is the set universe and $\theta$ is an equivalence relation on the set $U$ is called an approximation space. The equivalence relation $\theta$ is a relation that is reflexive, symmetric, and transitive. If the set $X \subseteq U$, then we can determine the upper approximation of the set $X$, denoted by $\overline{Apr}(X)$, and the lower approximation of the set $X$, denoted by $\underline{Apr}(X)$. The set $X$ is said to be a rough set on $(U, \theta)$ if and only if $\overline{Apr}(X)-\underline{Apr}(X) \neq \emptyset$. A rough set $X$ is a rough module if it satisfies certain axioms. This paper discusses the construction of a rough quotient module over a rough ring using the coset concept to determine its equivalence classes and discusses the properties of a rough quotient module over a rough ring related to a rough torsion module.
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Keywords: Approximation space; rough module; rough quotient module over rough ring; rough torsion module

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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