The distributivity spectrum of Baker's variety

TL;DR

This paper investigates the distributivity spectrum of Baker's variety, determining minimal congruence inclusion levels and exploring related identities in varieties with near-unanimity terms and reflexive relations.

Contribution

It provides a detailed evaluation of the smallest k for congruence inclusions in Baker's variety and studies identities involving near-unanimity terms and reflexive relations.

Findings

Determined minimal k for congruence inclusion in Baker's variety

Analyzed identities with near-unanimity terms

Discussed properties of reflexive and admissible relations

Abstract

For every $n$, we evaluate the smallest $k$ such that the congruence inclusion $\alpha (\beta \circ_n \gamma ) \subseteq \alpha \beta \circ_{k} \alpha \gamma $ holds in a variety of reducts of lattices introduced by K. Baker. We also study varieties with a near-unanimity term and discuss identities dealing with reflexive and admissible relations.