Characterizing the commutator in varieties with a difference term

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.

31 pages, 7 figures. Changes: revised title; one notational change to align with Andrew Moorhead's "Supernilpotent Taylor algebra are nilpotent," Trans. Amer. Math. Soc. 374 (2021), 1229-1276; expanded references; one problem added at end; a few typos fixed. To appear in Algebra Universalis