Single identities forcing lattices to be Boolean-Reference-Cited by-同舟云学术

Single identities forcing lattices to be Boolean

Published:2018-08-01 Issue:4 Volume:68 Page:713-716
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Chajda Ivan¹,Länger Helmut¹²,Padmanabhan Ranganathan³

Affiliation:

1. Department of Algebra and Geometry Faculty of Science , Palacký University Olomouc , 17. listopadu 12 771 46 , Olomouc , Czech Republic

2. Institute of Discrete Mathematics and Geometry , Faculty of Mathematics and Geoinformation TU Wien , Wiedner Hauptstraße 8–10 1040 , Vienna , Austria

3. Department of Mathematics , University of Manitoba , Winnipeg R3T 2N2 , Manitoba , Canada

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0138/pdf

Reference9 articles.

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2. Chajda, I.–Padmanabhan, R.: Lattices with unique complementation, Acta Sci. Math. (Szeged) 83 (2017), 31–34.

3. Dilworth, R. P.: Lattices with unique complements, Trans. Amer. Math. Soc. 57 (1945), 123–154.

4. Grätzer, G.: General Lattice Theory, Birkhäuser, Basel, 2003.

5. Huntington, E. V.: Sets of independent postulates for the algebra of logic, Trans. Amer. Math. Soc. 5 (1904), 288–309.

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