{"id":"https://openalex.org/W3019650816","doi":"https://doi.org/10.22331/q-2020-12-24-378","title":"The three types of normal sequential effect algebras","display_name":"The three types of normal sequential effect algebras","publication_year":2020,"publication_date":"2020-12-24","ids":{"openalex":"https://openalex.org/W3019650816","doi":"https://doi.org/10.22331/q-2020-12-24-378","mag":"3019650816"},"language":"lv","primary_location":{"id":"doi:10.22331/q-2020-12-24-378","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-12-24-378","pdf_url":"https://quantum-journal.org/papers/q-2020-12-24-378/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2020-12-24-378/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Abraham Westerbaan","orcid":null},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Abraham Westerbaan","raw_affiliation_strings":["Radboud Universiteit Nijmegen"],"affiliations":[{"raw_affiliation_string":"Radboud Universiteit Nijmegen","institution_ids":["https://openalex.org/I145872427"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Bas Westerbaan","orcid":null},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB","NL"],"is_corresponding":false,"raw_author_name":"Bas Westerbaan","raw_affiliation_strings":["Radboud Universiteit Nijmegen","University College London"],"affiliations":[{"raw_affiliation_string":"Radboud Universiteit Nijmegen","institution_ids":["https://openalex.org/I145872427"]},{"raw_affiliation_string":"University College London","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"last","author":{"id":null,"display_name":"John van de Wetering","orcid":"https://orcid.org/0000-0002-5405-8959"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"John van de Wetering","raw_affiliation_strings":["Radboud Universiteit Nijmegen"],"affiliations":[{"raw_affiliation_string":"Radboud Universiteit Nijmegen","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.5781,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.72582522,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"4","issue":null,"first_page":"378","last_page":"378"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.7384999990463257,"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":0.7384999990463257,"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":0.04899999871850014,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.043699998408555984,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/unit-interval","display_name":"Unit interval","score":0.6380000114440918},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.5878999829292297},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.557699978351593},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4652999937534332},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.43149998784065247},{"id":"https://openalex.org/keywords/subalgebra","display_name":"Subalgebra","score":0.4293000102043152},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.42800000309944153},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.42329999804496765},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4221000075340271}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7305999994277954},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.6380000114440918},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.5878999829292297},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.557699978351593},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4652999937534332},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.4293000102043152},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4221000075340271},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41370001435279846},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.39910000562667847},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3874000012874603},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3732999861240387},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.3531999886035919},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.352400004863739},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2994999885559082},{"id":"https://openalex.org/C100376341","wikidata":"https://www.wikidata.org/wiki/Q649977","display_name":"Jordan algebra","level":4,"score":0.29789999127388},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.288100004196167},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.27900001406669617},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C2776379255","wikidata":"https://www.wikidata.org/wiki/Q3406705","display_name":"Crossed product","level":3,"score":0.25040000677108765}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2020-12-24-378","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-12-24-378","pdf_url":"https://quantum-journal.org/papers/q-2020-12-24-378/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2004.12749","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.12749","pdf_url":"https://arxiv.org/pdf/2004.12749","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:132ce25e0b1941eca8cb59d8561541df","is_oa":true,"landing_page_url":"https://doaj.org/article/132ce25e0b1941eca8cb59d8561541df","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 4, p 378 (2020)","raw_type":"article"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/229650","is_oa":false,"landing_page_url":"https://hdl.handle.net/2066/229650","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, 4, pp. 1-23","raw_type":"Article / Letter to editor"},{"id":"pmh:ru:oai:repository.ubn.ru.nl:2066/229650","is_oa":true,"landing_page_url":"http://hdl.handle.net/2066/229650","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, 4, 1 - 23","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.22331/q-2020-12-24-378","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-12-24-378","pdf_url":"https://quantum-journal.org/papers/q-2020-12-24-378/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3019650816.pdf","grobid_xml":"https://content.openalex.org/works/W3019650816.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W144889459","https://openalex.org/W1980152963","https://openalex.org/W1983437996","https://openalex.org/W1987774407","https://openalex.org/W2017365165","https://openalex.org/W2021768421","https://openalex.org/W2024125908","https://openalex.org/W2031248193","https://openalex.org/W2040870895","https://openalex.org/W2046900812","https://openalex.org/W2058238486","https://openalex.org/W2066230022","https://openalex.org/W2077498699","https://openalex.org/W2077998048","https://openalex.org/W2080412456","https://openalex.org/W2087004189","https://openalex.org/W2093085284","https://openalex.org/W2103417273","https://openalex.org/W2110664297","https://openalex.org/W2129659010","https://openalex.org/W2165212773","https://openalex.org/W2165693845","https://openalex.org/W2219634533","https://openalex.org/W2234244214","https://openalex.org/W2259211523","https://openalex.org/W2267753132","https://openalex.org/W2326356851","https://openalex.org/W2326967362","https://openalex.org/W2530915168","https://openalex.org/W2607566499","https://openalex.org/W2654864742","https://openalex.org/W2733911839","https://openalex.org/W2761271237","https://openalex.org/W2792649776","https://openalex.org/W2795932065","https://openalex.org/W2888254535","https://openalex.org/W2911836321","https://openalex.org/W2928247742","https://openalex.org/W2940858033","https://openalex.org/W2950156064","https://openalex.org/W2951084199","https://openalex.org/W2962744501","https://openalex.org/W2964180607","https://openalex.org/W2992475894","https://openalex.org/W3030890936","https://openalex.org/W4205887594","https://openalex.org/W4211185072","https://openalex.org/W4293484738"],"related_works":[],"abstract_inverted_index":{"A":[0,33],"sequential":[1,52,242,266],"effect":[2,7],"algebra":[3,8,75,136],"(SEA)":[4],"is":[5,35],"an":[6,240],"equipped":[9],"with":[10,56,239],"a":[11,62,70,92,126,133,139,146,172,180,186,199,216,235],"<mml:math":[12,24,37,85,115,122,129,137,143,153,158],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[13,38,86,159],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[14,39,87,160],"class=\"MJX-tex-mathit\"":[15,40,88,161],"mathvariant=\"italic\">sequential":[16],"product</mml:mtext></mml:mrow></mml:math>":[17],"operation":[18],"modeled":[19],"after":[20],"the":[21,51,66,96,101,164,194,204,225,232,261,265],"L\u00fcders":[22],"product":[23,53,267],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo":[25],"stretchy=\"false\">(</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo":[26],"stretchy=\"false\">)</mml:mo><mml:mo":[27],"stretchy=\"false\">\u21a6</mml:mo><mml:msqrt><mml:mi>a</mml:mi></mml:msqrt><mml:mi>b</mml:mi><mml:msqrt><mml:mi>a</mml:mi></mml:msqrt></mml:math>":[28],"on":[29,61,100,260],"C<mml:math":[30],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msup><mml:mi":[31],"/><mml:mo>\u2217</mml:mo></mml:msup></mml:math>-algebras.":[32],"SEA":[34,121,142,152,173],"called":[36],"mathvariant=\"italic\">normal</mml:mtext></mml:mrow></mml:math>":[41],"when":[42,114],"it":[43],"has":[44],"all":[45],"suprema":[46],"of":[47,69,78,95,132,150,196,201,206,237,263],"directed":[48],"sets,":[49],"and":[50,65,145,183],"interacts":[54],"suitably":[55],"these":[57],"suprema.":[58],"The":[59],"effects":[60],"Hilbert":[63],"space":[64],"unit":[67,98],"interval":[68,99],"von":[71],"Neumann":[72],"or":[73],"JBW":[74],"are":[76,82,111],"examples":[77],"normal":[79,107,120,141,151,197,221,249],"SEAs":[80,108,198,222,238,250],"that":[81,118,171,223,246],"in":[83,268],"addition":[84],"mathvariant=\"italic\">convex</mml:mtext></mml:mrow></mml:math>,":[89],"i.e.":[90],"possess":[91],"suitable":[93],"action":[94],"real":[97],"algebra.":[102],"Complete":[103],"Boolean":[104,135,181],"algebras":[105],"form":[106],"too,":[109],"which":[110,174,190],"convex":[112,140],"only":[113,176],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>0</mml:mn><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>.We":[116],"show":[117],"any":[119],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>E</mml:mi></mml:math>":[123],"splits":[124],"as":[125],"direct":[127],"sum":[128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>\u2295</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>\u2295</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow":[130],"class=\"MJX-TeXAtom-ORD\"><mml:mi>a</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math>":[131,155],"complete":[134],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>E</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:math>,":[138],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>E</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>,":[144],"newly":[147],"identified":[148],"type":[149],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>E</mml:mi><mml:mrow":[154],"we":[156,166,184,191,214],"dub":[157],"mathvariant=\"italic\">purely":[162],"almost-convex</mml:mtext></mml:mrow></mml:math>.Along":[163],"way":[165],"show,":[167],"among":[168],"other":[169],"things,":[170],"contains":[175],"idempotents":[177],"must":[178],"be":[179,256,272],"algebra;":[182],"establish":[185],"spectral":[187],"theorem":[188],"using":[189],"settle":[192],"for":[193,220],"class":[195],"problem":[200],"Gudder":[202],"regarding":[203],"uniqueness":[205],"square":[207],"roots.":[208],"After":[209],"establishing":[210],"our":[211,252],"main":[212],"result,":[213],"propose":[215],"simple":[217],"extra":[218],"axiom":[219,254],"excludes":[224],"seemingly":[226],"pathological":[227],"a-convex":[228],"SEAs.":[229],"We":[230,244],"conclude":[231],"paper":[233],"by":[234],"study":[236],"associative":[241],"product.":[243],"find":[245],"associativity":[247],"forces":[248],"satisfying":[251],"new":[253],"to":[255],"commutative,":[257],"shedding":[258],"light":[259],"question":[262],"why":[264],"quantum":[269],"theory":[270],"should":[271],"non-associative.":[273]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2020-05-01T00:00:00"}