Year: 2025
Type: article
Abstract: For a composite number π, we explore a topological space on the ring of integers modulo π, we usebasis sets formed by solutions to quadratic residue equations,where elements are unitsmodulo π. This definitionallows us to investigate the algebraic relationships among solutions, focusing on properties like clopen sets, closure, and interior operations. Additionally, we examine the continuity of mappings between the group of units in β€/πβ€and quadratic residues, alongside the quotient topology induced on this group of units. Acomparison of the separation properties of these topological spaces is also presented.
Author: Hamza A. Daoub
Institution: Al Zawiya University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4410146618