An Application of the Separator of Subsets of Semigroups in the Number Theory

TL;DR

This paper introduces a new construction of special congruences on commutative semigroups and applies it to the multiplicative semigroup of positive integers, offering insights into number theory structures.

Contribution

It presents a novel method for constructing specific congruences on commutative semigroups and demonstrates its application to fundamental number theory semigroups.

Findings

New construction of congruences on commutative semigroups

Application to the multiplicative semigroup of positive integers

Potential implications for number theory

Abstract

In this paper we give a construction for a special type of congruences on commutative semigroups. We apply our result for the multiplicative semigroup of all positive integers.