Meet-reducible submaximal clones determined by two central relations

TL;DR

This paper characterizes specific central relations on finite sets where the combined clone of their preserving operations forms a maximal subclone of a fixed central relation's clone, advancing understanding of clone lattice structures.

Contribution

It identifies all central relations sigma for which the join of Pol(rho) and Pol(sigma) yields a maximal subclone of Pol(rho), given a fixed central relation rho.

Findings

Characterization of central relations sigma with maximal join clones

Complete description of submaximal clones determined by two central relations

Advancement in understanding the structure of clone lattices on finite sets

Abstract

Let rho and sigma be two central relations on a finite set A. It is known that the clones Pol(rho) and Pol(sigma) which consists of all operations on A that preserve rho respectively sigma are among the maximal clones on A. In this paper, we find all central relations sigma such that the join clone of Pol(rho) and Pol(sigma) is a maximal subclone of Pol(rho) where rho is a fixed central relation.