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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 2010): 06A11, 06A06, 06D15

DOI: 10.21136/MB.2017.0037-16

Full text available as PDF.

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