Counting finite semirings

TL;DR

This paper systematically counts finite semirings up to isomorphism and anti-isomorphism for small sizes using computational tools, providing a classification that enhances understanding of their structure.

Contribution

It introduces a method for enumerating finite semirings up to isomorphism and anti-isomorphism, leveraging existing semigroup libraries in GAP for small cases.

Findings

Complete counts of finite semirings for small sizes

Classification up to isomorphism and anti-isomorphism

Utilization of GAP Smallsemi library for enumeration

Abstract

In this short note we count the finite semirings up to isomorphism, and up to isomorphism and anti-isomorphism for some small values of $n$; for which we utilise the existing library of small semigroups in the GAP package Smallsemi.