English

Characterizing the commutator in varieties with a difference term

Rings and Algebras 2022-02-16 v3

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.

Cite

@article{arxiv.2112.00715,
  title  = {Characterizing the commutator in varieties with a difference term},
  author = {Keith A. Kearnes and Ágnes Szendrei and Ross Willard},
  journal= {arXiv preprint arXiv:2112.00715},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-24T08:00:12.156Z