Scheme theory for commutative semirings

TL;DR

This survey explores two methods for constructing affine schemes for commutative semirings, linking prime ideal and prime kernel approaches via universal valuations, to deepen understanding of their algebraic geometry.

Contribution

It compares prime ideal and prime kernel approaches to affine schemes for semirings and connects them through universal valuations, providing a unified perspective.

Findings

Two approaches to affine schemes are described: prime ideals and prime kernels.

The relationship between these approaches is established via universal valuations.

The survey clarifies the algebraic geometric structure of commutative semirings.

Abstract

In this survey, we describe two different approaches to constructing affine schemes for commutative semirings: one based on prime ideals, and another based on prime kernels (also called subtractive ideals). We then explain how these two approaches are related through the theory of universal valuations.