# Nearness Rings on Nearness Approximation Spaces

## TL;DR

This paper introduces the concept of nearness rings and ideals within nearness approximation spaces, defining algebraic structures and exploring homomorphisms to advance the mathematical framework of nearness theory.

## Contribution

It proposes a novel approach to define nearness rings, ideals, and homomorphisms on nearness approximation spaces, expanding the algebraic structure of nearness theory.

## Key findings

- Defined nearness rings and ideals using new operations on weak cosets
- Studied properties of nearness rings and ideals
- Explored nearness homomorphisms and their properties

## Abstract

In this paper, we consider the problem of how to establish algebraic structures on nearness approximation spaces. Essentially, our approach is to define the nearness ring, nearness ideal and nearness ring of all weak cosets by considering new operations on the set of all weak cosets. Afterwards, our aim is to study nearness homomorphism on nearness approximation spaces, and to investigate some properties of nearness rings and ideals.