Mathematica Bohemica, first online, pp. 9, 2017


Relatively pseudocomplemented posets

Ivan Chajda, Helmut Länger

Received March 4, 2016.  First published May 29, 2017.

Abstract:  We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relatively pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending chain condition and one more natural condition. Suitable examples are provided.
Keywords:  relatively pseudocomplemented poset; join-semilattice; distributive poset
Classification MSC:  06A11, 06A06, 06D15
DOI:  10.21136/MB.2017.0037-16

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Affiliations:   Ivan Chajda, Palacký University Olomouc, Faculty of Science, Department of Algebra and Geometry, 17. listopadu 12, 771 46 Olomouc, Czech Republic, e-mail: ivan.chajda@upol.cz; Helmut Länger, TU Wien, Fakultät für Mathematik und Geoinformation, Institut für Diskrete Mathematik und Geometrie, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria, e-mail: helmut.laenger@tuwien.ac.at


 
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