Monotone and cone preserving mappings on posets
Mathematica Bohemica (2023)
- Volume: 148, Issue: 2, page 197-210
- ISSN: 0862-7959
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topChajda, Ivan, and Länger, Helmut. "Monotone and cone preserving mappings on posets." Mathematica Bohemica 148.2 (2023): 197-210. <http://eudml.org/doc/299521>.
@article{Chajda2023,
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 study in which posets 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.},
author = {Chajda, Ivan, Länger, Helmut},
journal = {Mathematica Bohemica},
keywords = {poset; directed poset; semilattice; chain; monotone; strictly monotone; upper cone preserving; strictly upper cone preserving; strongly upper cone preserving; ordinal sum; induced equivalence relation},
language = {eng},
number = {2},
pages = {197-210},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Monotone and cone preserving mappings on posets},
url = {http://eudml.org/doc/299521},
volume = {148},
year = {2023},
}
TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
TI - Monotone and cone preserving mappings on posets
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 2
SP - 197
EP - 210
AB - We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to study in which posets 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.
LA - eng
KW - poset; directed poset; semilattice; chain; monotone; strictly monotone; upper cone preserving; strictly upper cone preserving; strongly upper cone preserving; ordinal sum; induced equivalence relation
UR - http://eudml.org/doc/299521
ER -
References
top- Berrone, L. R., 10.1007/s00010-020-00699-1, Aequationes Math. 94 (2020), 803-816. (2020) Zbl1448.39038MR4145720DOI10.1007/s00010-020-00699-1
- Chajda, I., 10.1142/S1793557108000059, Asian-Eur. J. Math. 1 (2008), 45-51. (2008) Zbl1159.06002MR2400299DOI10.1142/S1793557108000059
- Chajda, I., Goldstern, M., Länger, H., 10.1007/s00012-018-0517-9, Algebra Universalis 79 (2018), Paper No. 25, 7 pages. (2018) Zbl6904410MR3788204DOI10.1007/s00012-018-0517-9
- Chajda, I., Hošková, Š., 10.18514/MMN.2005.107, Miskolc Math. Notes 6 (2005), 147-152. (2005) Zbl1095.08001MR2199159DOI10.18514/MMN.2005.107
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