{"id":"https://openalex.org/W2095331324","doi":"https://doi.org/10.1142/s0218196709005196","title":"SUBALGEBRAS OF GOLOD\u2013SHAFAREVICH ALGEBRAS","display_name":"SUBALGEBRAS OF GOLOD\u2013SHAFAREVICH ALGEBRAS","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2095331324","doi":"https://doi.org/10.1142/s0218196709005196","mag":"2095331324"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005196","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005196","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":true,"oa_status":"green","oa_url":"https://escholarship.org/content/qt09q6f0hr/qt09q6f0hr.pdf?t=lq6oaj","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5097175911","display_name":"THOMAS VODEN","orcid":null},"institutions":[{"id":"https://openalex.org/I45135547","display_name":"Glendale Community College","ror":"https://ror.org/02e1syn97","country_code":"US","type":"education","lineage":["https://openalex.org/I45135547"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"THOMAS VODEN","raw_affiliation_strings":["Glendale College, 1500 North Verdugo Road, Glendale, CA 91208, USA"],"affiliations":[{"raw_affiliation_string":"Glendale College, 1500 North Verdugo Road, Glendale, CA 91208, USA","institution_ids":["https://openalex.org/I45135547"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5097175911"],"corresponding_institution_ids":["https://openalex.org/I45135547"],"apc_list":null,"apc_paid":null,"fwci":0.7565,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.69689142,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"03","first_page":"423","last_page":"442"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997000098228455,"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/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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8822098970413208},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.6205753684043884},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6063982844352722},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5344423651695251},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5163735151290894},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.470216304063797},{"id":"https://openalex.org/keywords/quadratic-algebra","display_name":"Quadratic algebra","score":0.44626352190971375},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3469679355621338},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.3409520089626312},{"id":"https://openalex.org/keywords/cellular-algebra","display_name":"Cellular algebra","score":0.24334204196929932},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04666537046432495}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8822098970413208},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.6205753684043884},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6063982844352722},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5344423651695251},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5163735151290894},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.470216304063797},{"id":"https://openalex.org/C104736235","wikidata":"https://www.wikidata.org/wiki/Q7268354","display_name":"Quadratic algebra","level":5,"score":0.44626352190971375},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3469679355621338},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.3409520089626312},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.24334204196929932},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04666537046432495},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196709005196","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005196","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"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt09q6f0hr","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/09q6f0hr","pdf_url":"https://escholarship.org/content/qt09q6f0hr/qt09q6f0hr.pdf?t=lq6oaj","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"}],"best_oa_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt09q6f0hr","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/09q6f0hr","pdf_url":"https://escholarship.org/content/qt09q6f0hr/qt09q6f0hr.pdf?t=lq6oaj","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2095331324.pdf"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W53998202","https://openalex.org/W2055530051","https://openalex.org/W2085546873","https://openalex.org/W2327127028","https://openalex.org/W4238667695"],"related_works":["https://openalex.org/W3037086953","https://openalex.org/W4312108621","https://openalex.org/W2320881711","https://openalex.org/W1677942884","https://openalex.org/W3145196301","https://openalex.org/W2592509875","https://openalex.org/W2187643696","https://openalex.org/W3004589026","https://openalex.org/W3186716778","https://openalex.org/W4300421559"],"abstract_inverted_index":{"A":[0,83,101,116],"graded":[1,38],"associative":[2],"algebra":[3,53,88],"generated":[4],"by":[5,55,90],"m":[6,22,56,91],"elements":[7],"of":[8,26,37,51,100,115],"degree":[9,27],"one":[10],"is":[11,17,72,84],"called":[12],"Golod\u2013Shafarevich":[13],"(GS)":[14],"if":[15,63,82,104,120],"it":[16],"presented":[18,54,89],"with":[19],"less":[20],"than":[21],"2":[23],"/4":[24],"relators":[25,60],"at":[28],"least":[29],"two.":[30],"We":[31,44,78],"explore":[32],"conditions":[33],"under":[34],"which":[35],"subalgebras":[36],"GS":[39,62,103,119],"algebras":[40],"are":[41,61,102,117],"themselves":[42],"GS.":[43],"prove":[45],"that":[46,81],"infinitely":[47],"many":[48,112],"Veronese":[49,98,113],"powers":[50,99,114],"an":[52],"generators":[57,92],"and":[58,93,108],"r":[59,94],"[Formula:":[64,75,105,121],"see":[65,76,106,122],"text].":[66,77,123],"For":[67],"quadratic":[68,87],"algebras,":[69],"the":[70],"bound":[71],"improved":[73],"to":[74],"also":[79],"show":[80],"a":[85],"generic":[86],"relators,":[95],"then":[96],"all":[97,109],"text],":[107],"but":[110],"finitely":[111],"not":[118]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
