{"id":"https://openalex.org/W4311923927","doi":"https://doi.org/10.1142/s0218196723500145","title":"\u21242-gradings and minimal varieties of \u21242-graded PI algebras","display_name":"\u21242-gradings and minimal varieties of \u21242-graded PI algebras","publication_year":2022,"publication_date":"2022-12-09","ids":{"openalex":"https://openalex.org/W4311923927","doi":"https://doi.org/10.1142/s0218196723500145"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196723500145","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196723500145","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/A5055183424","display_name":"Danilo Vilela Avelar","orcid":null},"institutions":[{"id":"https://openalex.org/I161127581","display_name":"Universidade Federal Fluminense","ror":"https://ror.org/02rjhbb08","country_code":"BR","type":"education","lineage":["https://openalex.org/I161127581"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Danilo Vilela Avelar","raw_affiliation_strings":["Departamento de An\u00e1lise, Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal Fluminense, 24210-201 NITER\u00d3I, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lise, Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal Fluminense, 24210-201 NITER\u00d3I, Brazil","institution_ids":["https://openalex.org/I161127581"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082347579","display_name":"Viviane Ribeiro Tomaz da Silva","orcid":"https://orcid.org/0000-0003-2543-2515"},"institutions":[{"id":"https://openalex.org/I110200422","display_name":"Universidade Federal de Minas Gerais","ror":"https://ror.org/0176yjw32","country_code":"BR","type":"education","lineage":["https://openalex.org/I110200422"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Viviane Ribeiro Tomaz da Silva","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Instituto de Ci\u00eancias Exatas, Universidade Federal de Minas Gerais, 30161-970 BELO HORIZONTE, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Instituto de Ci\u00eancias Exatas, Universidade Federal de Minas Gerais, 30161-970 BELO HORIZONTE, Brazil","institution_ids":["https://openalex.org/I110200422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082347579"],"corresponding_institution_ids":["https://openalex.org/I110200422"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27130828,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"02","first_page":"261","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"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":1.0,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9987000226974487,"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/T11308","display_name":"Sphingolipid Metabolism and Signaling","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8128452301025391},{"id":"https://openalex.org/keywords/superalgebra","display_name":"Superalgebra","score":0.661261796951294},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.6483715772628784},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4614357650279999},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.41181617975234985},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36751478910446167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32736605405807495},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.30339932441711426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8128452301025391},{"id":"https://openalex.org/C186863843","wikidata":"https://www.wikidata.org/wiki/Q3977654","display_name":"Superalgebra","level":3,"score":0.661261796951294},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.6483715772628784},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4614357650279999},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.41181617975234985},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36751478910446167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32736605405807495},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30339932441711426},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196723500145","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196723500145","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":[{"id":"https://openalex.org/G1969558435","display_name":null,"funder_award_id":"306534/2016-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8791776025","display_name":null,"funder_award_id":"APQ-01149-18","funder_id":"https://openalex.org/F4320322980","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320322980","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","ror":"https://ror.org/00nc55f03"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W70534879","https://openalex.org/W1776651865","https://openalex.org/W1967210055","https://openalex.org/W1985692289","https://openalex.org/W2037571535","https://openalex.org/W2044776378","https://openalex.org/W2057315263","https://openalex.org/W2970653357","https://openalex.org/W2974236804"],"related_works":["https://openalex.org/W2082917694","https://openalex.org/W2982131286","https://openalex.org/W3180765644","https://openalex.org/W4288061039","https://openalex.org/W4298349627","https://openalex.org/W1578159187","https://openalex.org/W2962977764","https://openalex.org/W1580888858","https://openalex.org/W1975260776","https://openalex.org/W2869201820"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,14,24,29,39,43,47,53,58,62,70,73,83,106,109,128,148,152,160,172,187],"see":[2,15,25,30,40,44,48,54,59,63,71,74,84,107,110,129,149,153,161,173,188],"text]":[3,16,31,41,49,55,162],"be":[4,17,103,164,197],"an":[5,132],"algebraically":[6],"closed":[7],"field":[8],"of":[9,105,138,151,171],"characteristic":[10],"zero":[11],"and":[12,50,88,92,122,177,181],"let":[13],"a":[18,33,119],"minimal":[19,86,104,175],"superalgebra":[20],"with":[21,61],"semisimple":[22],"part":[23],"text],":[26,60,64,72,154],"where":[27],"each":[28],"is":[32,42],"simple":[34],"superalgebra.":[35],"We":[36,141],"say":[37],"that":[38,57,126],"text]-special":[45,85,174],"if":[46],"there":[51],"exists":[52],"such":[56,100,120],"whereas,":[65],"for":[66,95,155,190],"the":[67,82,96,127,136,147,156,191],"remaining":[68],"indices":[69],"text].":[75,111],"In":[76,112],"[1],":[77],"Avelar":[78],"et":[79],"al.":[80],"classified":[81],"superalgebras":[87,101,176],"described":[89],"some":[90,139],"necessary":[91,180],"sufficient":[93,143,182],"conditions":[94,183],"varieties":[97,192],"generated":[98,158,193],"by":[99,159,194],"to":[102,118,163,196],"text]-exponent":[108],"this":[113],"paper,":[114],"we":[115,123,167,178],"give":[116,179],"continuity":[117],"study":[121],"made":[124],"explicit":[125],"text]-gradings":[130],"play":[131],"important":[133],"role":[134],"in":[135],"minimality":[137],"varieties.":[140],"provide":[142],"conditions,":[144],"depending":[145],"on":[146,185],"text]-grading":[150],"variety":[157],"minimal.":[165,198],"Moreover,":[166],"characterize":[168],"two":[169],"families":[170],"(depending":[184],"their":[186],"text]-gradings)":[189],"them":[195]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}