1. Relatively pseudocomplemented posets
- Creator:
- Chajda, Ivan and Länger, Helmut
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- relatively pseudocomplemented poset, join-semilattice, and distributive poset
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public