Algebraic Properties of Paraorthomodular Posets

被引：3

作者：

Chajda, Ivan ^{[1
]}

Fazio, Davide ^{[2
]}

Langer, Helmut ^{[1
,3
]}

Ledda, Antonio ^{[2
]}

Paseka, Jan ^{[4
]}

机构：

[1] Palacky Univ Olomouc, Dept Algebra & Geometry, Fac Sci, 17 Listopadu 12, Olomouc 77146, Czech Republic

[2] Univ Cagliari, ALoPHiS Res Grp, Via Mirrionis 1, I-09123 Cagliari, Italy

[3] TU Wien, Fac Math & Geoinformat, Inst Discrete Math & Geometry, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[4] Masaryk Univ Brno, Dept Math & Stat, Fac Sci, Kotlarska 2, Brno 61137, Czech Republic

来源：

LOGIC JOURNAL OF THE IGPL | 2022年 / 30卷 / 05期

基金：

奥地利科学基金会;

关键词：

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

D O I：

10.1093/jigpal/jzab024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：840 / 869

页数：30

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