Regular Antilattices

TL;DR

This paper studies and enumerates a special class of antilattices where certain Green's equivalences are congruences, providing a detailed algebraic analysis of their structure.

Contribution

It introduces and characterizes regular antilattices with all Green's equivalences as congruences, expanding understanding of their algebraic properties.

Findings

Enumeration of regular antilattices

Characterization of Green's equivalences as congruences

Structural insights into antilattice properties

Abstract

Antilattices $(S;\lor, \land)$ for which the Green's equivalences $\mathcal L_{(\lor)}$, $\mathcal R_{(\lor)}$, $\mathcal L_{(\land)}$ and $\mathcal R_{(\land)}$ are all congruences of the entire antilattice are studied and enumerated.