×

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.

MSC:

06A11 Algebraic aspects of posets
06A06 Partial orders, general
06D15 Pseudocomplemented lattices
PDF BibTeX XML Cite
Full Text: DOI