A note on minors determined by clones of semilattices

TL;DR

This paper investigates the structure of C-minor partial orders generated by clones of semilattice operations, proving they satisfy the descending chain condition, which has implications for their algebraic properties.

Contribution

It establishes that C-minor partial orders from clones of semilattices satisfy the descending chain condition, a new result in the study of algebraic structures.

Findings

C-minor partial orders satisfy the descending chain condition

Clones generated by semilattice operations have specific order-theoretic properties

Results contribute to understanding the algebraic and order-theoretic structure of semilattice clones

Abstract

The C-minor partial orders determined by the clones generated by a semilattice operation (and possibly the constant operations corresponding to its identity or zero elements) are shown to satisfy the descending chain condition.