Endomorphism semirings with zero of a finite semilattice of a special type

TL;DR

This paper studies the structure of endomorphism semirings of a specific type of finite semilattice, introducing new simple semirings and analyzing their algebraic properties.

Contribution

It constructs new finite simple semirings from a particular class of finite semilattices with a unique minimal and maximal element.

Findings

Identification of conditions for simplicity of endomorphism semirings

Construction of new finite simple semirings

Analysis of algebraic properties of these semirings

Abstract

We investigate endomorphism semirings of a finite semilattice with one least element and one greatest element such that all the other elements form an antichain. We construct some new finite simple semirings. Keywords: endomorphism semiring, additively idempotent semiring, simple semiring, idempotent endomorphism, finite semilattice.