A short way to directed J\'onsson terms

TL;DR

The paper proves that varieties with Jönsson terms also have directed Jönsson terms, resolving a previously posed problem and providing refined results for locally finite varieties.

Contribution

It establishes the existence of directed Jönsson terms in varieties with Jönsson terms, solving a notable open problem in universal algebra.

Findings

Directed Jönsson terms exist for varieties with Jönsson terms

Results apply to locally finite varieties

Addresses a problem raised by Kazda et al.

Abstract

We show that a variety with J\'onsson terms $t_1, \dots, t_{n-1}$ has directed J\'onsson terms $d_1, \dots, d_{n-1}$, for the same value of the indices, solving a problem raised by Kazda et al.. Refined results are obtained for locally finite varieties.