Characterizing the commutator in varieties with a difference term

TL;DR

This paper extends Kiss's characterization of the commutator to varieties with a difference term, addressing a gap in previous work and exploring properties of Kiss terms in such varieties.

Contribution

It generalizes the commutator characterization to a broader class of varieties and corrects prior inaccuracies in the literature.

Findings

Extended Kiss's characterization to varieties with a difference term

Fixed a gap in previous finite basis theorem paper

Proved properties of Kiss terms in these varieties

Abstract

We extend the validity of Kiss's characterization of the commutator from congruence modular varieties to varieties with a difference term. This fixes a recently discovered gap in our paper [A finite basis theorem for difference-term varieties with a finite residual bound, Trans. Amer. Math. Soc., 368 (2016), 2115--2143]. We also prove some related properties of Kiss terms in varieties with a difference term.