Suppose throughout that V is a congruence distributive variety. If m ≥ 1, let J V (m) be the smallest natural number k such that the congruence identity α(β ◦ γ ◦ β . . . ) ⊆ αβ ◦ αγ ◦ αβ ◦ . . . holds in V , with m occurrences of ◦ on the left and k occurrences of ◦ on the right. We show that if J V (m) = k, then J V (m) ≤ k, for every natural number . If J V (1) = 2, that is, V is 3-distributive, then J V (m) ≤ m, for every m ≥ 3. If V is m-modular, that is, congruence modularity of V is witnessed by m + 1 Day terms, then J V (2) ≤ J V (1) + 2m 2 − 2m − 1. Open problems are stated at various places.

Lipparini, P. (2018). The Jónsson distributivity spectrum. ALGEBRA UNIVERSALIS, 79(2) [10.1007/s00012-018-0491-2].

The Jónsson distributivity spectrum

Lipparini, Paolo
2018-01-01

Abstract

Suppose throughout that V is a congruence distributive variety. If m ≥ 1, let J V (m) be the smallest natural number k such that the congruence identity α(β ◦ γ ◦ β . . . ) ⊆ αβ ◦ αγ ◦ αβ ◦ . . . holds in V , with m occurrences of ◦ on the left and k occurrences of ◦ on the right. We show that if J V (m) = k, then J V (m) ≤ k, for every natural number . If J V (1) = 2, that is, V is 3-distributive, then J V (m) ≤ m, for every m ≥ 3. If V is m-modular, that is, congruence modularity of V is witnessed by m + 1 Day terms, then J V (2) ≤ J V (1) + 2m 2 − 2m − 1. Open problems are stated at various places.
2018
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
English
Con Impact Factor ISI
Congruence distributive variety; (directed) Jónsson terms; Jónsson distributivity spectrum; Congruence identity; Identities for reflexive and admissible relations
Lipparini, P. (2018). The Jónsson distributivity spectrum. ALGEBRA UNIVERSALIS, 79(2) [10.1007/s00012-018-0491-2].
Lipparini, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/207928
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