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.
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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