Congruence modular and congruence distributive varieties can be characterized by the existence of sequences of Gumm and Jónsson terms, respectively. Such sequences have variable lengths, in general. It is immediate from the above paragraph that there is a variety with Gumm terms but without Jónsson terms. We prove the unexpected result that, on the other hand, if some variety has both kinds of terms, then the minimal lengths of the sequences differ at most by 1. It follows that every congruence distributive variety with (r+1) Day terms has (r^2-r+3) Jónsson terms.

Lipparini, P. (2020). The Gumm level equals the alvin level in congruence distributive varieties. ARCHIV DER MATHEMATIK, 115, 391-400 [10.1007/s00013-020-01503-x].

### The Gumm level equals the alvin level in congruence distributive varieties

#### Abstract

Congruence modular and congruence distributive varieties can be characterized by the existence of sequences of Gumm and Jónsson terms, respectively. Such sequences have variable lengths, in general. It is immediate from the above paragraph that there is a variety with Gumm terms but without Jónsson terms. We prove the unexpected result that, on the other hand, if some variety has both kinds of terms, then the minimal lengths of the sequences differ at most by 1. It follows that every congruence distributive variety with (r+1) Day terms has (r^2-r+3) Jónsson terms.
##### Scheda breve Scheda completa Scheda completa (DC)
9-lug-2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Gumm terms; alvin terms; Jónsson terms; congruence distributive variety; congruence modular variety; congruence identity
https://arxiv.org/abs/2001.06705
Lipparini, P. (2020). The Gumm level equals the alvin level in congruence distributive varieties. ARCHIV DER MATHEMATIK, 115, 391-400 [10.1007/s00013-020-01503-x].
Lipparini, P
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Descrizione: expanded version with new results in the appendix
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