Orthomodular and Skew Orthomodular Posets

Autor:	Ivan Chajda, Miroslav Kolařík, Helmut Länger
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	smallest non-lattice orthomodular poset skew orthomodular poset Boolean poset horizontal sum compatibility relation commutator Mathematics QA1-939
Zdroj:	Symmetry, Vol 15, Iss 4, p 810 (2023)
Druh dokumentu:	article
ISSN:	2073-8994
DOI:	10.3390/sym15040810
Popis:	We present the smallest non-lattice orthomodular poset and show that it is unique up to isomorphism. Since not every Boolean poset is orthomodular, we consider the class of skew orthomodular posets previously introduced by the first and third author under the name “generalized orthomodular posets”. We show that this class contains all Boolean posets and we study its subclass consisting of horizontal sums of Boolean posets. For this purpose, we introduce the concept of a compatibility relation and the so-called commutator of two elements. We show the relationship between these concepts and introduce a kind of ternary discriminator for horizontal sums of Boolean posets. Numerous examples illuminating these concepts and results are included in the paper.
Databáze:	Directory of Open Access Journals
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