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VARIETIES OF SKEW BOOLEAN ALGEBRAS WITH INTERSECTIONS

Part of: Varieties

Published online by Cambridge University Press:  09 September 2016

JONATHAN LEECH  and
MATTHEW SPINKS
JONATHAN LEECH
Affiliation:
Department of Mathematics, Westmont College, Santa Barbara, CA 93018, USA email [email protected]
MATTHEW SPINKS*
Affiliation:
Department of Philosophy, University of Cagliari, Cagliari 09123, Italy email [email protected]
*
✉[email protected]
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Abstract

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Skew Boolean algebras for which pairs of elements have natural meets, called intersections, are studied from a universal algebraic perspective. Their lattice of varieties is described and shown to coincide with the lattice of quasi-varieties. Some connections of relevance to arbitrary skew Boolean algebras are also established.

Keywords

skew Boolean algebrasintersections(sub)directly irreducible algebraslattice of (quasi-)varietiesdiscriminator varieties

MSC classification

Primary: 08B15: Lattices of varieties
Secondary: 06E75: Generalizations of Boolean algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 2 , April 2017 , pp. 290 - 306
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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