A topological description of the space of prime ideals of a monoid

TL;DR

This paper characterizes the topological spaces that can be realized as the prime spectrum of a commutative monoid, extending classical results in algebraic topology and algebraic geometry.

Contribution

It provides a topological classification of prime spectra of monoids, linking algebraic structures to topological properties in a novel way.

Findings

Identifies conditions for a topological space to be a prime spectrum of a monoid

Extends Hochster's and Brenner's theses to monoids

Provides a framework for understanding monoid spectra topologically

Abstract

We describe which topological spaces can arise as the prime spectrum of a commutative monoid, in the spirit of Hochster's and Brenner's theses.