Relatively pseudocomplemented posets. (English) Zbl 1463.06006

Summary: 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.


06A11 Algebraic aspects of posets
06A06 Partial orders, general
06D15 Pseudocomplemented lattices
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