Extreme representations of semirings

TL;DR

This paper summarizes discussions on the classification of irreducible representations across different semirings, focusing on their extreme or fundamental forms, based on a study group held at Uppsala University.

Contribution

It provides a comprehensive overview of the classification of irreducible representations of semirings, highlighting new approaches and open problems discussed during the study group.

Findings

Classification schemes for irreducible semiring representations

Identification of key properties of 'extreme' representations

Open problems in semiring representation theory

Abstract

This is a write-up of the discussions during the meetings of the study group on representation theory of semirings which was organized at the Department of Mathematics, Uppsala University, during the academic year 2017-2018. The main emphasis is on classification of various classes of "irreducible" representations for various concrete semirings.