| Title:
|
Monotone and cone preserving mappings on posets (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Länger, Helmut |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
197-210 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
poset |
| Keyword:
|
directed poset |
| Keyword:
|
semilattice |
| Keyword:
|
chain |
| Keyword:
|
monotone |
| Keyword:
|
strictly monotone |
| Keyword:
|
upper cone preserving |
| Keyword:
|
strictly upper cone preserving |
| Keyword:
|
strongly upper cone preserving |
| Keyword:
|
ordinal sum |
| Keyword:
|
induced equivalence relation |
| MSC:
|
06A06 |
| MSC:
|
06A11 |
| MSC:
|
06A12 |
| idZBL:
|
Zbl 07729572 |
| idMR:
|
MR4585576 |
| DOI:
|
10.21136/MB.2022.0026-21 |
| . |
| Date available:
|
2023-05-04T17:57:11Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151684 |
| . |
| Reference:
|
[1] Berrone, L. R.: The homomorphism equation on semilattices.Aequationes Math. 94 (2020), 803-816. Zbl 1448.39038, MR 4145720, 10.1007/s00010-020-00699-1 |
| Reference:
|
[2] Chajda, I.: Homomorphisms of directed posets.Asian-Eur. J. Math. 1 (2008), 45-51. Zbl 1159.06002, MR 2400299, 10.1142/S1793557108000059 |
| Reference:
|
[3] Chajda, I., Goldstern, M., Länger, H.: A note on homomorphisms between products of algebras.Algebra Universalis 79 (2018), Paper No. 25, 7 pages. Zbl 6904410, MR 3788204, 10.1007/s00012-018-0517-9 |
| Reference:
|
[4] Chajda, I., Hošková, Š.: A characterization of cone preserving mappings of quasiordered sets.Miskolc Math. Notes 6 (2005), 147-152. Zbl 1095.08001, MR 2199159, 10.18514/MMN.2005.107 |
| . |
