Geodesic
Relatively pseudocomplemented posets
Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 89-97

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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.
DOI : 10.21136/MB.2017.0037-16
Classification : 06A06, 06A11, 06D15
Keywords: relatively pseudocomplemented poset; join-semilattice; distributive poset 
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Chajda, Ivan; Länger, Helmut. Relatively pseudocomplemented posets. Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 89-97. doi: 10.21136/MB.2017.0037-16

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