{"id":"https://openalex.org/W2039928244","doi":"https://doi.org/10.1002/malq.19990450206","title":"Distributive Lattices with a Negation Operator","display_name":"Distributive Lattices with a Negation Operator","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2039928244","doi":"https://doi.org/10.1002/malq.19990450206","mag":"2039928244"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19990450206","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19990450206","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076062079","display_name":"Sergio A. Celani","orcid":"https://orcid.org/0000-0003-2542-4128"},"institutions":[{"id":"https://openalex.org/I3130805194","display_name":"Universidad Nacional del Centro de la Provincia de Buenos Aires","ror":"https://ror.org/011gakh74","country_code":"AR","type":"education","lineage":["https://openalex.org/I3130805194"]}],"countries":["AR"],"is_corresponding":true,"raw_author_name":"Sergio Arturo Celani","raw_affiliation_strings":["Departamento de Matematica, Facultad de Ciencias Exactas Universidad Nacional del Centro, Pinto 399, 7000 Tandil, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matematica, Facultad de Ciencias Exactas Universidad Nacional del Centro, Pinto 399, 7000 Tandil, Argentina","institution_ids":["https://openalex.org/I3130805194"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076062079"],"corresponding_institution_ids":["https://openalex.org/I3130805194"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.1735914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"45","issue":"2","first_page":"207","last_page":"218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":1.0,"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":1.0,"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9965999722480774,"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/distributive-property","display_name":"Distributive property","score":0.8330520391464233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8152814507484436},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.779261589050293},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.7393807172775269},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5476101040840149},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.5331966280937195},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5141932964324951},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.48270082473754883},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.47261905670166016},{"id":"https://openalex.org/keywords/operator-algebra","display_name":"Operator algebra","score":0.45178067684173584},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4359603822231293},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4263383746147156},{"id":"https://openalex.org/keywords/complete-lattice","display_name":"Complete lattice","score":0.42312395572662354},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40502673387527466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3490487337112427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06166529655456543}],"concepts":[{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.8330520391464233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8152814507484436},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.779261589050293},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.7393807172775269},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5476101040840149},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.5331966280937195},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5141932964324951},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.48270082473754883},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.47261905670166016},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.45178067684173584},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4359603822231293},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4263383746147156},{"id":"https://openalex.org/C201640847","wikidata":"https://www.wikidata.org/wiki/Q2362924","display_name":"Complete lattice","level":3,"score":0.42312395572662354},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40502673387527466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3490487337112427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06166529655456543},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19990450206","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19990450206","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W124628085","https://openalex.org/W1991442995","https://openalex.org/W1991748341","https://openalex.org/W2023648368","https://openalex.org/W2033904092","https://openalex.org/W2047897946","https://openalex.org/W2053013736","https://openalex.org/W2061686800","https://openalex.org/W2069397469","https://openalex.org/W2140351059","https://openalex.org/W3047122219","https://openalex.org/W3202100200","https://openalex.org/W4293176479"],"related_works":["https://openalex.org/W3007066267","https://openalex.org/W2944618814","https://openalex.org/W1975062576","https://openalex.org/W2383799344","https://openalex.org/W2044636175","https://openalex.org/W2065881966","https://openalex.org/W2280679128","https://openalex.org/W2147371450","https://openalex.org/W1776047664","https://openalex.org/W2126448176"],"abstract_inverted_index":{"Abstract":[0],"In":[1,69],"this":[2],"note":[3],"we":[4,71,85],"introduce":[5],"and":[6,33,50,63,75],"study":[7],"algebras":[8,62],"(":[9,22],"L":[10,23],",":[11,24],"V,":[12,25],"\u039b,":[13],"\u231d,":[14,26],"0,1)":[15,27],"of":[16,78,91],"type":[17],"(2,":[18],"2,1,1,1)":[19],"such":[20,79],"that":[21,38],"is":[28,35],"a":[29,47,67],"bounded":[30],"distributive":[31],"lattice":[32],"\u231d":[34,42,48,51],"an":[36,80,83],"operator":[37],"satisfies":[39],"the":[40,57,73,76,88],"condition":[41],"(a":[43],"V":[44],"b)":[45],"=":[46,53],"b":[49],"0":[52],"1.":[54],"We":[55],"develop":[56],"topological":[58],"duality":[59],"between":[60],"these":[61],"Priestley":[64,89],"spaces":[65,90],"with":[66],"relation.":[68],"addition,":[70],"characterize":[72],"congruences":[74],"subalgebras":[77],"algebra.":[81],"As":[82],"application,":[84],"will":[86],"determine":[87],"quasi\u2010Stone":[92],"algebras.":[93]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-07T14:30:12.667765","created_date":"2025-10-10T00:00:00"}
