{"id":"https://openalex.org/W4361007365","doi":"https://doi.org/10.3390/sym15040810","title":"Orthomodular and Skew Orthomodular Posets","display_name":"Orthomodular and Skew Orthomodular Posets","publication_year":2023,"publication_date":"2023-03-27","ids":{"openalex":"https://openalex.org/W4361007365","doi":"https://doi.org/10.3390/sym15040810"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040810","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040810","pdf_url":"https://www.mdpi.com/2073-8994/15/4/810/pdf?version=1680061726","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/4/810/pdf?version=1680061726","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005373819","display_name":"Ivan Chajda","orcid":"https://orcid.org/0000-0003-3840-3879"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Ivan Chajda","raw_affiliation_strings":["Department of Algebra and Geometry, Faculty of Science, Palack\u00fd University Olomouc, 771 46 Olomouc, Czech Republic"],"raw_orcid":"https://orcid.org/0000-0003-3840-3879","affiliations":[{"raw_affiliation_string":"Department of Algebra and Geometry, Faculty of Science, Palack\u00fd University Olomouc, 771 46 Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101950308","display_name":"Miroslav Kola\u0159\u00edk","orcid":"https://orcid.org/0000-0002-0641-4584"},"institutions":[{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Miroslav Kola\u0159\u00edk","raw_affiliation_strings":["Department of Computer Science, Faculty of Science, Palack\u00fd University Olomouc, 771 46 Olomouc, Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Faculty of Science, Palack\u00fd University Olomouc, 771 46 Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063985495","display_name":"Helmut L\u00e4nger","orcid":"https://orcid.org/0000-0002-7030-4080"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]},{"id":"https://openalex.org/I70703428","display_name":"Palack\u00fd University Olomouc","ror":"https://ror.org/04qxnmv42","country_code":"CZ","type":"education","lineage":["https://openalex.org/I70703428"]}],"countries":["AT","CZ"],"is_corresponding":true,"raw_author_name":"Helmut L\u00e4nger","raw_affiliation_strings":["Department of Algebra and Geometry, Faculty of Science, Palack\u00fd University Olomouc, 771 46 Olomouc, Czech Republic","Institute of Discrete Mathematics and Geometry, Faculty of Mathematics and Geoinformation, Technische Universit\u00e4t Wien, 1040 Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0002-7030-4080","affiliations":[{"raw_affiliation_string":"Department of Algebra and Geometry, Faculty of Science, Palack\u00fd University Olomouc, 771 46 Olomouc, Czech Republic","institution_ids":["https://openalex.org/I70703428"]},{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, Faculty of Mathematics and Geoinformation, Technische Universit\u00e4t Wien, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063985495"],"corresponding_institution_ids":["https://openalex.org/I145847075","https://openalex.org/I70703428"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04329567,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"4","first_page":"810","last_page":"810"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7414237856864929},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.7339841723442078},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.5329006314277649},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5313521027565002},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.5116724967956543},{"id":"https://openalex.org/keywords/star-product","display_name":"Star product","score":0.5039359927177429},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4561253786087036},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3871842622756958},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18463125824928284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7414237856864929},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.7339841723442078},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.5329006314277649},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5313521027565002},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5116724967956543},{"id":"https://openalex.org/C195800304","wikidata":"https://www.wikidata.org/wiki/Q7601281","display_name":"Star product","level":2,"score":0.5039359927177429},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4561253786087036},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3871842622756958},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18463125824928284},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040810","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040810","pdf_url":"https://www.mdpi.com/2073-8994/15/4/810/pdf?version=1680061726","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4cd98d54172d4ad489d4a911207e01ae","is_oa":false,"landing_page_url":"https://doaj.org/article/4cd98d54172d4ad489d4a911207e01ae","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 4, p 810 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/810/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040810","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15040810","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040810","pdf_url":"https://www.mdpi.com/2073-8994/15/4/810/pdf?version=1680061726","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7599999904632568,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3688524014","display_name":null,"funder_award_id":"I 4579-N","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G3858672000","display_name":null,"funder_award_id":"20-09869L","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7620661493","display_name":null,"funder_award_id":"20-09869L","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G7649835187","display_name":null,"funder_award_id":"I 4579-N","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4361007365.pdf"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1818487909","https://openalex.org/W2158076586","https://openalex.org/W2610241812","https://openalex.org/W3037204522","https://openalex.org/W3085043350","https://openalex.org/W3126996113","https://openalex.org/W4210335350","https://openalex.org/W4210535193","https://openalex.org/W6638457782"],"related_works":["https://openalex.org/W4254064397","https://openalex.org/W3033029084","https://openalex.org/W2957182409","https://openalex.org/W3143802155","https://openalex.org/W2015965805","https://openalex.org/W2789323833","https://openalex.org/W1975173901","https://openalex.org/W4300914096","https://openalex.org/W3131828648","https://openalex.org/W61453168"],"abstract_inverted_index":{"We":[0,45,84],"present":[1],"the":[2,25,34,40,71,78,86,114],"smallest":[3],"non-lattice":[4],"orthomodular":[5,29,43],"poset":[6,20],"and":[7,36,54,77,91,109],"show":[8,46,85],"that":[9,47],"it":[10],"is":[11,21],"unique":[12],"up":[13],"to":[14],"isomorphism.":[15],"Since":[16],"not":[17],"every":[18],"Boolean":[19,52,64,102],"orthomodular,":[22],"we":[23,55,69],"consider":[24],"class":[26,49],"of":[27,60,63,73,81,95,101],"skew":[28],"posets":[30,53],"previously":[31],"introduced":[32],"by":[33],"first":[35],"third":[37],"author":[38],"under":[39],"name":[41],"\u201cgeneralized":[42],"posets\u201d.":[44],"this":[48,67],"contains":[50],"all":[51],"study":[56],"its":[57],"subclass":[58],"consisting":[59],"horizontal":[61,99],"sums":[62,100],"posets.":[65,103],"For":[66],"purpose,":[68],"introduce":[70,92],"concept":[72],"a":[74,93],"compatibility":[75],"relation":[76],"so-called":[79],"commutator":[80],"two":[82],"elements.":[83],"relationship":[87],"between":[88],"these":[89,107],"concepts":[90,108],"kind":[94],"ternary":[96],"discriminator":[97],"for":[98],"Numerous":[104],"examples":[105],"illuminating":[106],"results":[110],"are":[111],"included":[112],"in":[113],"paper.":[115]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
