{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T21:48:58Z","timestamp":1772574538935,"version":"3.50.1"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T00:00:00Z","timestamp":1625702400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,9,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>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\u2013MacNeille completion is paraorthomodular are provided.<\/jats:p>","DOI":"10.1093\/jigpal\/jzab024","type":"journal-article","created":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T19:22:43Z","timestamp":1623266563000},"page":"840-869","source":"Crossref","is-referenced-by-count":7,"title":["Algebraic Properties of Paraorthomodular Posets"],"prefix":"10.1093","volume":"30","author":[{"given":"Ivan","family":"Chajda","sequence":"first","affiliation":[{"name":"Faculty of Science Department of Algebra and Geometry, Palack\u00fd University Olomouc , 17. listopadu 12, 771 46 Olomouc, Czech Republic"}]},{"given":"Davide","family":"Fazio","sequence":"additional","affiliation":[{"name":"A.Lo.P.Hi.S Research Group, University of Cagliari Via Is Mirrionis 1 , 09123 Cagliari, Italy"}]},{"given":"Helmut","family":"L\u00e4nger","sequence":"additional","affiliation":[{"name":"TU Wien Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry , Wiedner Hauptstra\u00dfe 8-10, 1040 Vienna, Austria, and Faculty of Science Department of Algebra and Geometry, Palack\u00fd University Olomouc, 17. listopadu 12, 771 46 Olomouc, Czech Republic"}]},{"given":"Antonio","family":"Ledda","sequence":"additional","affiliation":[{"name":"A.Lo.P.Hi.S Research Group University of Cagliari Via Is Mirrionis 1 , 09123 Cagliari, Italy"}]},{"given":"Jan","family":"Paseka","sequence":"additional","affiliation":[{"name":"Faculty of Science Department of Mathematics and Statistics, Masaryk University Brno , Kotl\u00e1\u0159sk\u00e1 2, 611 37 Brno, Czech Republic"}]}],"member":"286","published-online":{"date-parts":[[2021,7,8]]},"reference":[{"key":"2022092120485122300_ref1","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1017\/S144678870000598X","article-title":"A note on a paper of D. 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