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THE DISTRIBUTIVITY SPECTRUM OF BAKER’S VARIETY

Part of: Varieties Lattices

Published online by Cambridge University Press:  26 October 2020

PAOLO LIPPARINI Open the ORCID record for PAOLO LIPPARINI [Opens in a new window]
PAOLO LIPPARINI*
Affiliation:
Dipartimento Fornace di Matematica, Viale della Ricerca Scientifica, Università di Roma ‘Tor Vergata’, I-00133RomeItaly
*
e-mail: lipparin@axp.mat.uniroma2.it
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Abstract

For every n, we evaluate the smallest k such that the congruence inclusion $\alpha (\beta \circ _n \gamma ) \subseteq \alpha \beta \circ _{k} \alpha \gamma $ holds in a variety of reducts of lattices introduced by K. Baker. We also study varieties with a near-unanimity term and discuss identities dealing with reflexive and admissible relations.

Keywords

Baker’s varietyJónsson distributivity spectrumcongruence identityrelation identitycongruence distributive varietynear-unanimity termedge term

MSC classification

Primary: 08B10: Congruence modularity, congruence distributivity
Secondary: 06B75: Generalizations of lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 110 , Issue 1 , February 2021 , pp. 119 - 144
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by James East

Work performed under the auspices of G.N.S.A.G.A. Work supported by PRIN 2012 ‘Logica, Modelli e Insiemi’. The author acknowledges the MIUR Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.

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