{"id":"https://openalex.org/W2042387325","doi":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","title":"A Question of Foulser on \u03bb-Systems of Characteristic Two","display_name":"A Question of Foulser on \u03bb-Systems of Characteristic Two","publication_year":1969,"publication_date":"1969-05-01","ids":{"openalex":"https://openalex.org/W2042387325","doi":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","mag":"2042387325"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9939-1969-0240717-8","doi":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","pdf_url":"https://www.ams.org/proc/1969-021-02/S0002-9939-1969-0240717-8/S0002-9939-1969-0240717-8.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/proc/1969-021-02/S0002-9939-1969-0240717-8/S0002-9939-1969-0240717-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068310375","display_name":"M. L. Narayana Rao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. L. Narayana Rao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058892772","display_name":"Joseph L. Zemmer","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. L. Zemmer","raw_affiliation_strings":["University of Missouri, Columbia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Missouri, Columbia","institution_ids":["https://openalex.org/I76835614"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.19572108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"2","first_page":"373","last_page":"373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.40549999475479126,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.40549999475479126,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.33500000834465027,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.07029999792575836,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lambda-system","display_name":"Lambda system","score":0.6439999938011169},{"id":"https://openalex.org/keywords/finite-projective-planes","display_name":"finite projective planes","score":0.6359999775886536},{"id":"https://openalex.org/keywords/nonassociative-division-algebras","display_name":"nonassociative division algebras","score":0.6470000147819519},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.32899999618530273}],"concepts":[{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.353939414024353},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.33880871534347534},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.2674645781517029}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0002-9939-1969-0240717-8","doi":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","pdf_url":"https://www.ams.org/proc/1969-021-02/S0002-9939-1969-0240717-8/S0002-9939-1969-0240717-8.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/2037007","doi":"https://doi.org/10.2307/2037007","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2037007","pdf_url":null,"source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0002-9939-1969-0240717-8","doi":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1969-0240717-8","pdf_url":"https://www.ams.org/proc/1969-021-02/S0002-9939-1969-0240717-8/S0002-9939-1969-0240717-8.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2042387325.pdf","grobid_xml":"https://content.openalex.org/works/W2042387325.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2912325219"],"related_works":["https://openalex.org/W2093294195","https://openalex.org/W1991139219","https://openalex.org/W7009882975","https://openalex.org/W2343331399","https://openalex.org/W4232263332","https://openalex.org/W2031977723","https://openalex.org/W2031462449","https://openalex.org/W1517670829","https://openalex.org/W4293070960","https://openalex.org/W2394562296"],"abstract_inverted_index":{"In":[0],"a":[1,9,130],"recent":[2],"paper":[3,191],"[l],":[4],"D.":[5],"A.":[6],"Foulser":[7,40],"described":[8],"general":[10],"construction":[11,131],"of":[12,50,69,96,115,132,134,148,166,172,212,214],"finite":[13,27],"(left)":[14],"Veblen-Wedderburn":[15],"systems":[16],"which":[17],"contain":[18],"the":[19,22,26,60,84,112,123,167,204,209],"nonexceptional":[20],"near-fields,":[21],"Andre":[23],"VW":[24,33],"systems,":[25,29],"Moulton":[28],"and":[30,79,153,169,184],"other":[31],"new":[32],"systems.At":[34],"one":[35,180],"point":[36],"in":[37,59,122,128,185],"his":[38],"work":[39],"wishes":[41],"to":[42,118,187,200],"know":[43],"whether":[44,89],"or":[45,90],"not":[46,91],"there":[47,65,92],"exist":[48,93],"Xsystems":[49],"order":[51,70,97,135,186],"26":[52],"with":[53,72,99,137,179],"kern":[54,73,100,138],"GF(2).He":[55],"answers":[56],"this":[57,116,120,190],"question":[58,121],"negative":[61],"by":[62],"proving":[63],"that":[64],"is":[66,111,144,175,198],"no":[67],"X-system":[68],"2d,":[71,98],"GF(2),":[74,101],"where":[75,102,140],"d":[76,103,154],"=":[77,142],"axbv":[78],"a,":[80],"b":[81],"are":[82],"primes.At":[83],"same":[85],"time":[86],"he":[87],"asks":[88],"proper":[94],"X-systems":[95,133,174],"contains":[104,155],"more":[105],"than":[106],"two":[107,206],"distinct":[108,159],"prime":[109,151,160],"factors.It":[110],"main":[113],"object":[114],"note":[117],"answer":[119],"affirmative.More":[124],"generally":[125],"we":[126],"give":[127],"\u00a71":[129],"qd,":[136],"GF(q),":[139],"q":[141],"p'":[143],"an":[145,149,163],"arbitrary":[146,150],"power":[147],"p,":[152],"at":[156,202],"least":[157],"three":[158],"factors.In":[161],"\u00a72":[162],"interesting":[164],"property":[165],"left":[168],"middle":[170],"nuclei":[171],"these":[173],"described.Foulser's":[176],"notation":[177],"is,":[178],"exception,":[181],"followed":[182],"throughout,":[183],"save":[188],"space":[189],"cannot":[192],"be":[193],"read":[194],"independently.In":[195],"particular,":[196],"it":[197],"necessary":[199],"have":[201],"hand":[203],"first":[205,210],"sections":[207],"plus":[208],"lemma":[211],"\u00a75":[213],"Foulser's":[215],"paper.":[216]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
