Mitschke's Theorem is sharp
Rings and Algebras
2022-01-25 v3
Abstract
A. Mitschke showed that a variety with an -ary near-unanimity term has J\'onsson terms witnessing congruence distributivity. We show that Mitschke's result is sharp. We also evaluate the best possible number of Day terms witnessing congruence modularity. More generally, we characterize exactly the best bounds for many congruence identities satisfied by varieties with an -ary near-unanimity term.
Cite
@article{arxiv.1909.00863,
title = {Mitschke's Theorem is sharp},
author = {Paolo Lipparini},
journal= {arXiv preprint arXiv:1909.00863},
year = {2022}
}
Comments
v2 a few improvements, some simplifications, some exemplifications v3 minor fixes, a few improvements, some more notions introduced