Single identities forcing lattices to be Boolean

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

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Orthomodular lattices that are horizontal sums of Boolean algebras;Commentationes Mathematicae Universitatis Carolinae;2020-05-22

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