{"id":"https://openalex.org/W4280603326","doi":"https://doi.org/10.1007/s11083-023-09648-4","title":"General Mixed Lattices","display_name":"General Mixed Lattices","publication_year":2023,"publication_date":"2023-09-27","ids":{"openalex":"https://openalex.org/W4280603326","doi":"https://doi.org/10.1007/s11083-023-09648-4"},"language":"en","primary_location":{"id":"doi:10.1007/s11083-023-09648-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-023-09648-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09648-4.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09648-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037522243","display_name":"Jani Jokela","orcid":"https://orcid.org/0000-0002-9036-1330"},"institutions":[{"id":"https://openalex.org/I166825849","display_name":"Tampere University","ror":"https://ror.org/033003e23","country_code":"FI","type":"education","lineage":["https://openalex.org/I166825849"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Jani Jokela","raw_affiliation_strings":["Mathematics, Faculty of Information Technology and Communication Sciences, Tampere University, PO. Box 692, 33101, Tampere, Finland"],"raw_orcid":"https://orcid.org/0000-0002-9036-1330","affiliations":[{"raw_affiliation_string":"Mathematics, Faculty of Information Technology and Communication Sciences, Tampere University, PO. Box 692, 33101, Tampere, Finland","institution_ids":["https://openalex.org/I166825849"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037522243"],"corresponding_institution_ids":["https://openalex.org/I166825849"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00936006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"3","first_page":"579","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9837999939918518,"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":0.9837999939918518,"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":0.008899999782443047,"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":0.0017000000225380063,"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/congruence-lattice-problem","display_name":"Congruence lattice problem","score":0.7350005507469177},{"id":"https://openalex.org/keywords/map-of-lattices","display_name":"Map of lattices","score":0.6960210800170898},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.676589846611023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6114023923873901},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5323697924613953},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.5125625133514404},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.5082647204399109},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.4746202528476715},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4278988242149353},{"id":"https://openalex.org/keywords/lattice-field-theory","display_name":"Lattice field theory","score":0.4147162139415741},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.33075571060180664},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3222811818122864},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18557143211364746},{"id":"https://openalex.org/keywords/reciprocal-lattice","display_name":"Reciprocal lattice","score":0.1855490803718567},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1110098659992218},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09375962615013123},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09082669019699097},{"id":"https://openalex.org/keywords/diffraction","display_name":"Diffraction","score":0.06595447659492493}],"concepts":[{"id":"https://openalex.org/C84540187","wikidata":"https://www.wikidata.org/wiki/Q5160997","display_name":"Congruence lattice problem","level":4,"score":0.7350005507469177},{"id":"https://openalex.org/C128379363","wikidata":"https://www.wikidata.org/wiki/Q6753757","display_name":"Map of lattices","level":4,"score":0.6960210800170898},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.676589846611023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6114023923873901},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5323697924613953},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.5125625133514404},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.5082647204399109},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.4746202528476715},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4278988242149353},{"id":"https://openalex.org/C42238305","wikidata":"https://www.wikidata.org/wiki/Q5370778","display_name":"Lattice field theory","level":3,"score":0.4147162139415741},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.33075571060180664},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3222811818122864},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18557143211364746},{"id":"https://openalex.org/C89957378","wikidata":"https://www.wikidata.org/wiki/Q164129","display_name":"Reciprocal lattice","level":3,"score":0.1855490803718567},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1110098659992218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09375962615013123},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09082669019699097},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.06595447659492493},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s11083-023-09648-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-023-09648-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09648-4.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2205.09064","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.09064","pdf_url":"https://arxiv.org/pdf/2205.09064","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:trepo.tuni.fi:10024/207336","is_oa":true,"landing_page_url":"https://trepo.tuni.fi/handle/10024/207336","pdf_url":null,"source":{"id":"https://openalex.org/S7407055260","display_name":"Trepo - Institutional Repository of Tampere University","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.48550/arxiv.2205.09064","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2205.09064","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s11083-023-09648-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-023-09648-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-023-09648-4.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Order","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280603326.pdf"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W150866053","https://openalex.org/W1989939605","https://openalex.org/W2046394361","https://openalex.org/W3094956099","https://openalex.org/W4294862433","https://openalex.org/W4362577282"],"related_works":["https://openalex.org/W669770","https://openalex.org/W3230280","https://openalex.org/W1426642","https://openalex.org/W4778887","https://openalex.org/W1106190","https://openalex.org/W9107303","https://openalex.org/W5605128","https://openalex.org/W64637951","https://openalex.org/W43242085","https://openalex.org/W31000174"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"mixed":[2,46,59,83,92,95],"lattice":[3,24,47,96],"is":[4],"a":[5,10,21,45,104],"lattice-type":[6],"structure":[7],"consisting":[8],"of":[9,20,44,58,74,91,107],"set":[11,106],"with":[12],"two":[13],"partial":[14],"orderings,":[15],"and":[16,37,61,79,94,100,111],"generalizing":[17],"the":[18,40,55,62,65,72,75,112],"notion":[19,43],"lattice.":[22],"Mixed":[23],"theory":[25],"has":[26],"previously":[27],"been":[28],"studied":[29],"in":[30,82],"various":[31,66],"algebraic":[32,110],"structures,":[33],"such":[34],"as":[35,98],"groups":[36,97],"semigroups,":[38],"while":[39],"more":[41],"general":[42],"remains":[48],"unexplored.":[49],"In":[50,68],"this":[51],"paper,":[52],"we":[53,70],"study":[54],"fundamental":[56],"properties":[57],"lattices":[60,93],"relationships":[63],"between":[64],"properties.":[67],"particular,":[69],"establish":[71],"equivalence":[73],"one-sided":[76],"associative,":[77],"distributive":[78],"modular":[80],"laws":[81],"lattices.":[84],"We":[85],"also":[86],"give":[87],"an":[88],"alternative":[89],"definition":[90],"non-commutative":[99],"non-associative":[101],"algebras":[102],"satisfying":[103],"certain":[105],"postulates.":[108],"The":[109],"order-theoretic":[113],"definitions":[114],"are":[115],"then":[116],"shown":[117],"to":[118],"be":[119],"equivalent.":[120]},"counts_by_year":[],"updated_date":"2026-01-20T17:24:06.736184","created_date":"2022-05-22T00:00:00"}
