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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 4

Issues

Single identities forcing lattices to be Boolean

Ivan Chajda
  • Department of Algebra and Geometry Faculty of Science, Palacký University Olomouc, 17. listopadu 12 771 46, Olomouc, Czech Republic
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/ Helmut Länger
  • Corresponding author
  • Department of Algebra and Geometry Faculty of Science, Palacký University Olomouc, 17. listopadu 12 771 46, Olomouc, Czech Republic
  • Institute of Discrete Mathematics and Geometry, Faculty of Mathematics and Geoinformation TU Wien, Wiedner Hauptstraße 8–10 1040, Vienna, Austria
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/ Ranganathan Padmanabhan
Published Online: 2018-08-06 | DOI: https://doi.org/10.1515/ms-2017-0138

Abstract

In this note we characterize Boolean algebras among lattices of type (2, 2, 1) with join, meet and an additional unary operation by means of single two-variable respectively three-variable identities. In particular, any uniquely complemented lattice satisfying any one of these equational constraints is distributive and hence a Boolean algebra.

MSC 2010: Primary 06C15; 06D05; 06E05

Keywords: complemented lattice; Boolean algebra; single axiom

Support of the research of both authors by ÖAD, project CZ 04/2017, and IGA, project PřF 2018 012, and of the second author by the Austrian Science Fund (FWF), project I 1923 N25, is gratefully acknowledged. The third author thanks Dr. Stephen Kirkland and the Department of Mathematics, University of Manitoba, for providing support and a pleasant atmosphere conducive of doing productive research.

References

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About the article

Received: 2016-10-07

Accepted: 2017-06-15

Published Online: 2018-08-06

Published in Print: 2018-08-28


Communicated by Mirko Navara


Citation Information: Mathematica Slovaca, Volume 68, Issue 4, Pages 713–716, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0138.

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