Monotone and cone preserving mappings on posets

DOI10.21136/MB.2022.0026-21arXiv2102.13109OpenAlexW3135488172MaRDI QIDQ6133024

Publication date: 17 August 2023

Published in: Mathematica Bohemica (Search for Journal in Brave)

Abstract: We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to characterize posets in which some of these mappings coincide. We define special mappings determined by two elements and investigate when these are strictly monotone or upper cone preserving. If the considered poset is a semilattice then its monotone mappings coincide with semilattice homomorphisms if and only if the poset is a chain. Similarly, we study posets which need not be semilattices but whose upper cones have a minimal element. We extend this investigation to posets that are direct products of chains or an ordinal sum of an antichain and a finite chain. We characterize equivalence relations induced by strongly monotone mappings and show that the quotient set of a poset by such an equivalence relation is a poset again.

Full work available at URL: https://arxiv.org/abs/2102.13109

zbMATH Keywords

monotone poset semilattice chain ordinal sum directed poset strictly monotone induced equivalence relation strictly upper cone preserving strongly upper cone preserving upper cone preserving

Mathematics Subject Classification ID

Partial orders, general (06A06) Algebraic aspects of posets (06A11) Semilattices (06A12)