Year: 2025
Type: article
Abstract: We study ideals and filters of posets and of pseudocomplemented posets and show a version of the Separation Theorem, known for ideals and filters in lattices and semilattices, within this general setting. We extend the concept of a $$*$$ -ideal already introduced by Rao for pseudocomplemented distributive lattices and by Talukder, Chakraborty and Begum for pseudocomplemented semilattices to pseudocomplemented posets. We derive several important properties of such ideals. Especially, we explain connections between prime filters, ultrafilters, filters satisfying the $$*$$ -condition and dense elements. Finally, we prove a Separation Theorem for $$*$$ -ideals.
Source: Soft Computing
Authors: Ivan Chajda, Helmut Länger
Institutions: Palacký University Olomouc, TU Wien
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4415746885