Between an $n$-ary and an $n{+}1$-ary near-unanimity term

TL;DR

This paper introduces a new algebraic condition that lies between the existence of n-ary and (n+1)-ary near-unanimity terms, and precisely determines the associated distributivity and modularity levels.

Contribution

It proposes a novel intermediate condition for near-unanimity terms and evaluates its implications for algebraic lattice properties.

Findings

Identifies a condition between n-ary and (n+1)-ary near-unanimity terms.

Determines the exact distributivity and modularity levels implied by this condition.

Abstract

We devise a condition strictly between the existence of an $n$-ary and an $n{+}1$-ary near-unanimity term. We evaluate exactly the distributivity and modularity levels implied by such a condition.