{"id":"https://openalex.org/W2133452007","doi":"https://doi.org/10.1142/s0218196707004323","title":"EVANS' NORMAL FORM THEOREM REVISITED","display_name":"EVANS' NORMAL FORM THEOREM REVISITED","publication_year":2007,"publication_date":"2007-12-01","ids":{"openalex":"https://openalex.org/W2133452007","doi":"https://doi.org/10.1142/s0218196707004323","mag":"2133452007"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196707004323","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196707004323","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5068463429","display_name":"Jonathan D. H. Smith","orcid":"https://orcid.org/0000-0002-2075-0744"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"JONATHAN D. H. SMITH","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, Iowa 50011-2064, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011-2064, USA","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068463429"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":0.4455,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.63939817,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":"08","first_page":"1577","last_page":"1592"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9993000030517578,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9695000052452087,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/triality","display_name":"Triality","score":0.9049508571624756},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8731561899185181},{"id":"https://openalex.org/keywords/quasigroup","display_name":"Quasigroup","score":0.8490311503410339},{"id":"https://openalex.org/keywords/idempotence","display_name":"Idempotence","score":0.7510905265808105},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5216482281684875},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5097012519836426},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4832904636859894},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.41745516657829285}],"concepts":[{"id":"https://openalex.org/C83716740","wikidata":"https://www.wikidata.org/wiki/Q17104294","display_name":"Triality","level":2,"score":0.9049508571624756},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8731561899185181},{"id":"https://openalex.org/C198800484","wikidata":"https://www.wikidata.org/wiki/Q1503423","display_name":"Quasigroup","level":2,"score":0.8490311503410339},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.7510905265808105},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5216482281684875},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5097012519836426},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4832904636859894},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.41745516657829285},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196707004323","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196707004323","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W77819666","https://openalex.org/W305406493","https://openalex.org/W644556536","https://openalex.org/W1574042277","https://openalex.org/W1964323576","https://openalex.org/W1975812750","https://openalex.org/W1976434884","https://openalex.org/W1979101142","https://openalex.org/W2007880116","https://openalex.org/W2021570669","https://openalex.org/W2026760906","https://openalex.org/W2073205225","https://openalex.org/W2083159970","https://openalex.org/W2092435222","https://openalex.org/W2128754484","https://openalex.org/W2152951761","https://openalex.org/W2326433233","https://openalex.org/W2487255306","https://openalex.org/W2804219209","https://openalex.org/W4230919050","https://openalex.org/W4249574695"],"related_works":["https://openalex.org/W2949500231","https://openalex.org/W46986720","https://openalex.org/W4231348199","https://openalex.org/W2063684714","https://openalex.org/W1998921562","https://openalex.org/W2133452007","https://openalex.org/W4287586461","https://openalex.org/W2588994260","https://openalex.org/W2066367484","https://openalex.org/W2952074770"],"abstract_inverted_index":{"Evans":[0],"defined":[1,78],"quasigroups":[2,24,77,94],"equationally,":[3],"and":[4,40,64],"proved":[5],"a":[6],"Normal":[7,61,85],"Form":[8,62],"Theorem":[9],"solving":[10],"the":[11,45,57,72,82,89],"word":[12],"problem":[13],"for":[14,88],"free":[15],"extensions":[16],"of":[17,44,59,71,76,81,92],"partial":[18],"Latin":[19],"squares.":[20],"In":[21],"this":[22],"paper,":[23],"are":[25,95],"redefined":[26],"as":[27,37,97],"algebras":[28],"with":[29],"six":[30,73],"basic":[31],"operations":[32],"related":[33],"by":[34,79],"triality,":[35],"manifested":[36],"coupled":[38],"right":[39],"left":[41],"regular":[42],"actions":[43],"symmetric":[46,83],"group":[47],"on":[48],"three":[49],"symbols.":[50],"Triality":[51],"leads":[52],"to":[53,69],"considerable":[54],"simplifications":[55],"in":[56],"proof":[58],"Evans'":[60],"Theorem,":[63],"makes":[65],"it":[66],"directly":[67],"applicable":[68],"each":[70],"major":[74],"varieties":[75,91],"subgroups":[80],"group.":[84],"form":[86],"theorems":[87],"corresponding":[90],"idempotent":[93],"obtained":[96],"immediate":[98],"corollaries.":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}