Algebraic Properties of Paraorthomodular Posets

J 2022

Algebraic Properties of Paraorthomodular Posets

CHAJDA, Ivan; Davide FAZIO; Helmut LÄNGER; Antonio LEDDA; Jan PASEKA et al.

Základní údaje

Originální název

Algebraic Properties of Paraorthomodular Posets

Autoři

CHAJDA, Ivan; Davide FAZIO; Helmut LÄNGER; Antonio LEDDA a Jan PASEKA

Vydání

Logic Journal of the IGPL, Oxford University Press, 2022, 1367-0751

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.000

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/22:00127892

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

poset with an antitone involution; orthomodular lattice; orthomodular poset; paraorthomodular lattice; paraorthomodular poset; orthoalgebra; effect algebra; commutative directoid; D-continuous poset; Dedekind-MacNeille completion

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 11. 7. 2023 10:01, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind–MacNeille completion is paraorthomodular are provided.

Návaznosti

MUNI/G/1211/2017, interní kód MU

Název: Grupové techniky a kvantová informace (Akronym: GRUPIK)

Investor: Masarykova univerzita, Grupové techniky a kvantová informace, INTERDISCIPLINARY - Mezioborové výzkumné projekty

Citovat

CHAJDA, Ivan; Davide FAZIO; Helmut LÄNGER; Antonio LEDDA a Jan PASEKA. Algebraic Properties of Paraorthomodular Posets. Logic Journal of the IGPL. Oxford University Press, 2022, roč. 30, č. 5, s. 840-869. ISSN 1367-0751. Dostupné z: https://doi.org/10.1093/jigpal/jzab024.

@article{2245566,
   author = {Chajda, Ivan and Fazio, Davide and Länger, Helmut and Ledda, Antonio and Paseka, Jan},
   article_number = {5},
   doi = {https://doi.org/10.1093/jigpal/jzab024},
   keywords = {poset with an antitone involution; orthomodular lattice; orthomodular poset; paraorthomodular lattice; paraorthomodular poset; orthoalgebra; effect algebra; commutative directoid; D-continuous poset; Dedekind-MacNeille completion},
   language = {eng},
   issn = {1367-0751},
   journal = {Logic Journal of the IGPL},
   title = {Algebraic Properties of Paraorthomodular Posets},
   url = {https://academic.oup.com/jigpal/article/30/5/840/6317499},
   volume = {30},
   year = {2022}
}

TY  - JOUR
ID  - 2245566
AU  - Chajda, Ivan - Fazio, Davide - Länger, Helmut - Ledda, Antonio - Paseka, Jan
PY  - 2022
TI  - Algebraic Properties of Paraorthomodular Posets
JF  - Logic Journal of the IGPL
VL  - 30
IS  - 5
SP  - 840-869
EP  - 840-869
PB  - Oxford University Press
SN  - 13670751
KW  - poset with an antitone involution
KW  - orthomodular lattice
KW  - orthomodular poset
KW  - paraorthomodular lattice
KW  - paraorthomodular poset
KW  - orthoalgebra
KW  - effect algebra
KW  - commutative directoid
KW  - D-continuous poset
KW  - Dedekind-MacNeille completion
UR  - https://academic.oup.com/jigpal/article/30/5/840/6317499
N2  - Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind–MacNeille completion is paraorthomodular are provided.
ER  -

CHAJDA, Ivan; Davide FAZIO; Helmut LÄNGER; Antonio LEDDA a Jan PASEKA. Algebraic Properties of Paraorthomodular Posets. \textit{Logic Journal of the IGPL}. Oxford University Press, 2022, roč.~30, č.~5, s.~840-869. ISSN~1367-0751. Dostupné z: https://doi.org/10.1093/jigpal/jzab024.

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