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A Characterization of Varieties with a Difference Term, II: Neutral = Meet Semi-Distributive

Published online by Cambridge University Press:  20 November 2018

Paolo Lipparini
Paolo Lipparini*
Affiliation:
Dipartimento di Matematica II Università di Roma (Tor Vergata) Viale della Ricerca ascientifica I-00133 Rome Italy, e-mail: lipparin@axp.mat.utovrm.it , lipparini@unica.it
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Abstract

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We provide more characterizations of varieties with a weak difference term and of neutral varieties. We prove that a variety has a (weak) difference term (is neutral) with respect to the $\text{TC}$-commutator iff it has a (weak) difference term (is neutral) with respect to the linear commutator. We show that a variety $V$ is congruence meet semi-distributive iff $V$ is neutral, iff ${{M}_{3}}$ is not a sublattice of Con $\mathbf{A}$, for $\mathbf{A}\in V$, iff there is a positive integer $n$ such that $V{{\vDash }_{Con}}\alpha (\beta \,o\,\gamma )\le \alpha {{\beta }_{n}}$.

Keywords

08B0508B99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 318 - 327
Copyright
Copyright © Canadian Mathematical Society 1998

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