{"id":"https://openalex.org/W2963001135","doi":"https://doi.org/10.1142/s021819671750045x","title":"Automorphic equivalence in the classical varieties of linear algebras","display_name":"Automorphic equivalence in the classical varieties of linear algebras","publication_year":2017,"publication_date":"2017-09-22","ids":{"openalex":"https://openalex.org/W2963001135","doi":"https://doi.org/10.1142/s021819671750045x","mag":"2963001135"},"language":"en","primary_location":{"id":"doi:10.1142/s021819671750045x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671750045x","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/A5020108868","display_name":"A. Tsurkov","orcid":null},"institutions":[{"id":"https://openalex.org/I35046152","display_name":"Universidade Federal do Rio Grande do Norte","ror":"https://ror.org/04wn09761","country_code":"BR","type":"education","lineage":["https://openalex.org/I35046152"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"A. Tsurkov","raw_affiliation_strings":["CCET, Mathematics Department, UFRN, Av. Senador Salgado Filho, 3000, Campus Universit\u00e1rio, Lagoa Nova, CEP 59078-970, Natal, RN, Brazil","Institute of Mathematics and Statistics, University S\u00e3o Paulo, Rua do Mat\u00e3o, 1010, Cidade Universit\u00e1ria, CEP 05508-090, S\u00e3o Paulo, SP, Brazil"],"affiliations":[{"raw_affiliation_string":"CCET, Mathematics Department, UFRN, Av. Senador Salgado Filho, 3000, Campus Universit\u00e1rio, Lagoa Nova, CEP 59078-970, Natal, RN, Brazil","institution_ids":["https://openalex.org/I35046152"]},{"raw_affiliation_string":"Institute of Mathematics and Statistics, University S\u00e3o Paulo, Rua do Mat\u00e3o, 1010, Cidade Universit\u00e1ria, CEP 05508-090, S\u00e3o Paulo, SP, Brazil","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020108868"],"corresponding_institution_ids":["https://openalex.org/I35046152"],"apc_list":null,"apc_paid":null,"fwci":2.3044,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.88097426,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"08","first_page":"973","last_page":"999"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9993000030517578,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9993000030517578,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9958999752998352,"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/T10849","display_name":"Finite Group Theory Research","score":0.9955000281333923,"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/mathematics","display_name":"Mathematics","score":0.882015585899353},{"id":"https://openalex.org/keywords/quotient-algebra","display_name":"Quotient algebra","score":0.7406294941902161},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6674422025680542},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5848619937896729},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.5602977871894836},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.412203848361969},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3691260814666748},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.19331437349319458}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.882015585899353},{"id":"https://openalex.org/C51287006","wikidata":"https://www.wikidata.org/wiki/Q63565120","display_name":"Quotient algebra","level":4,"score":0.7406294941902161},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6674422025680542},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5848619937896729},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5602977871894836},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.412203848361969},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3691260814666748},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.19331437349319458},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819671750045x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819671750045x","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1538534850","https://openalex.org/W1967654302","https://openalex.org/W1990767082","https://openalex.org/W1997326292","https://openalex.org/W2023761377","https://openalex.org/W2061741468","https://openalex.org/W2068665471","https://openalex.org/W2079918233","https://openalex.org/W2117933272","https://openalex.org/W2962705218","https://openalex.org/W2963112430","https://openalex.org/W2963283155","https://openalex.org/W3103590956","https://openalex.org/W4234165903","https://openalex.org/W4254660365","https://openalex.org/W4301172050"],"related_works":["https://openalex.org/W2072365522","https://openalex.org/W4307786893","https://openalex.org/W2372520984","https://openalex.org/W4311623600","https://openalex.org/W2901484729","https://openalex.org/W2950873203","https://openalex.org/W4298221493","https://openalex.org/W4289293717","https://openalex.org/W2081846106","https://openalex.org/W2385825362"],"abstract_inverted_index":{"This":[0],"research":[1],"is":[2,72,106,123,208,237,252],"a":[3,73,107,124,248],"continuation":[4],"of":[5,9,26,51,54,65,75,81,109,113,126,130,150,160,167,185,199,221,226,235,242,257,260,263,273,276,290],"[Tsurkov,":[6,164],"Automorphic":[7,165],"equivalence":[8,47,50,146,149,166,289],"linear":[10,27,168,201,277],"algebras,":[11,169,292],"J.":[12,170],"Algebra":[13,171],"Appl.":[14,172],"13(7)":[15,173],"(2014),":[16,174],"doi:10.1142/S0219498814500261].":[17],"In":[18,87,266],"this":[19,88,131,161,192],"paper,":[20,89],"we":[21,58,90,269],"consider":[22],"some":[23,271],"classical":[24],"varieties":[25,95,198],"algebras":[28,53,80,151,202,278,295],"over":[29],"the":[30,42,45,52,76,82,93,96,111,114,140,144,153,180,183,200,203,222,227,240,243,249,255,258,261,264,274,281,287],"field":[31],"[Formula:":[32,37,61,69,84,99,103,116,120,136,155,205,229],"see":[33,38,62,70,85,100,104,117,121,137,156,190,206,230],"text]":[34,63,71,105,118,122,138,207],"such":[35,279],"that":[36,194,280],"text].":[39,86,157,231],"We":[40,188],"study":[41],"relation":[43],"between":[44,143],"geometric":[46,145],"and":[48,119,147,163,247],"automorphic":[49,148,288],"these":[55,66,291,294],"varieties.":[56],"If":[57],"denote":[59],"by":[60,210,215,245],"one":[64],"varieties,":[67],"then":[68],"category":[74,115,228],"finite":[77],"generated":[78,209],"free":[79],"variety":[83,154],"calculate":[91],"for":[92],"considered":[94,197,282],"quotient":[97,134],"group":[98,108,135,204],"text],":[101],"where":[102],"all":[110,127,196],"automorphisms":[112,129,225,236,285],"subgroup":[125],"inner":[128],"category.":[132],"The":[133,158,232],"measures":[139],"possible":[141],"difference":[142],"from":[152,191],"results":[159],"paper":[162],"doi:":[175],"10.1142/S0219498814500261]":[176],"are":[177,213,296],"summarized":[178],"in":[179,195],"table":[181,193],"at":[182],"end":[184],"Sec.":[186,267],"5.":[187],"can":[189],"cosets":[211],"which":[212],"presented":[214],"no":[216],"more":[217],"than":[218],"two":[219],"types":[220],"strongly":[223,283],"stable":[224,284],"first":[233],"type":[234,251],"connected":[238,253],"with":[239,254],"changing":[241,256],"multiplication":[244,259],"scalar":[246],"second":[250],"elements":[262],"algebras.":[265],"6,":[268],"present":[270],"examples":[272],"pairs":[275],"provide":[286],"but":[293],"not":[297],"geometrically":[298],"equivalent.":[299]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}