Digital semigroups

TL;DR

This paper explores the connections between numerical monoids and specific subsemigroups of nonzero integers' multiplicative semigroup using base expansion techniques.

Contribution

It introduces a novel approach linking rational integer expansions to the structure of numerical monoids and related semigroups.

Findings

Established new relations between numerical monoids and subsemigroups of integers.

Provided insights into the algebraic structure of these semigroups.

Extended the understanding of integer base expansions in algebraic contexts.

Abstract

The well-known expansion of rational integers in an arbitrary integer base different from $0, 1, -1$ is exploited to study relations between numerical monoids and certain subsemigroups of the multiplicative semigroup of nonzero integers.