The finite basis problem for additively idempotent semirings of order four, II

TL;DR

This paper investigates the finite basis problem for 4-element additively idempotent semirings with specific additive structures, showing most are finitely based except one particular case.

Contribution

It classifies all such semirings up to isomorphism and determines which are finitely based, advancing understanding of their algebraic properties.

Findings

93 such semirings identified

All but one semiring are finitely based

Provides classification up to isomorphism

Abstract

We study the finite basis problem for $4$-element additively idempotent semirings whose additive reducts are quasi-antichains. Up to isomorphism, there are $93$ such algebras. We show that with the exception of the semiring $S_{(4, 435)}$, all of them are finitely based.