{"id":"https://openalex.org/W2038666859","doi":"https://doi.org/10.2307/2274479","title":"Differentially algebraic group chunks","display_name":"Differentially algebraic group chunks","publication_year":1990,"publication_date":"1990-09-01","ids":{"openalex":"https://openalex.org/W2038666859","doi":"https://doi.org/10.2307/2274479","mag":"2038666859"},"language":"en","primary_location":{"id":"doi:10.2307/2274479","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274479","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5110147319","display_name":"Anand Pillay","orcid":"https://orcid.org/0000-0002-2471-4097"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anand Pillay","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556","University of Notre Dame"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110147319"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":0.3764,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.6156406,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"55","issue":"3","first_page":"1138","last_page":"1142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9962000250816345,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9962000250816345,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9889000058174133,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/algebraically-closed-field","display_name":"Algebraically closed field","score":0.8036873936653137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7082164883613586},{"id":"https://openalex.org/keywords/algebraic-closure","display_name":"Algebraic closure","score":0.6298299431800842},{"id":"https://openalex.org/keywords/noetherian","display_name":"Noetherian","score":0.5910021066665649},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.567376971244812},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5298072099685669},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5277876257896423},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5255978107452393},{"id":"https://openalex.org/keywords/differential-algebra","display_name":"Differential algebra","score":0.5227030515670776},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5062112212181091},{"id":"https://openalex.org/keywords/algebraic-group","display_name":"Algebraic group","score":0.5042432546615601},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.4998817443847656},{"id":"https://openalex.org/keywords/transcendental-number","display_name":"Transcendental number","score":0.4647841453552246},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.43630677461624146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39183107018470764},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.29857581853866577},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1621285378932953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15777844190597534},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14768442511558533},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.1086500883102417}],"concepts":[{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.8036873936653137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7082164883613586},{"id":"https://openalex.org/C182327082","wikidata":"https://www.wikidata.org/wiki/Q428290","display_name":"Algebraic closure","level":5,"score":0.6298299431800842},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.5910021066665649},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.567376971244812},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5298072099685669},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5277876257896423},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5255978107452393},{"id":"https://openalex.org/C139080492","wikidata":"https://www.wikidata.org/wiki/Q7756337","display_name":"Differential algebra","level":2,"score":0.5227030515670776},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5062112212181091},{"id":"https://openalex.org/C187173678","wikidata":"https://www.wikidata.org/wiki/Q1695400","display_name":"Algebraic group","level":3,"score":0.5042432546615601},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4998817443847656},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.4647841453552246},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.43630677461624146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39183107018470764},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29857581853866577},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1621285378932953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15777844190597534},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14768442511558533},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.1086500883102417},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274479","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274479","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183743411","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743411","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1593399533","https://openalex.org/W1984427756","https://openalex.org/W1998136456","https://openalex.org/W2107348130","https://openalex.org/W2316875327"],"related_works":["https://openalex.org/W143396627","https://openalex.org/W3014738239","https://openalex.org/W2981814095","https://openalex.org/W4298098186","https://openalex.org/W2087623002","https://openalex.org/W2953042745","https://openalex.org/W2887669829","https://openalex.org/W3113030941","https://openalex.org/W1543976448","https://openalex.org/W2086001190"],"abstract_inverted_index":{"We":[0],"point":[1],"out":[2],"that":[3,102],"a":[4,10,26,35,69,76,80,107,154,159,175,182,186,192,202],"group":[5,29,73,77],"first":[6],"order":[7],"definable":[8,50,196],"in":[9,51,79,94,137,189,194],"differentially":[11,27,41,81,125,155,176,225],"closed":[12,42,53,82,126,156,177,226],"field":[13,157,214],"K":[14,31,173,181],"of":[15,25,40,44,86,99,124,128,140,198,224,228],"characteristic":[16,129,229],"0":[17,130],"can":[18,67],"be":[19],"definably":[20],"equipped":[21,163],"with":[22,164],"the":[23,38,87,103,138,165,195,212],"structure":[24],"algebraic":[28,72],"over":[30,153],".":[32,169,238],"This":[33],"is":[34,46,101,131,158,174,193,231],"translation":[36,88],"into":[37],"framework":[39],"fields":[43,54,127,142,227],"what":[45],"known":[47],"for":[48],"groups":[49],"algebraically":[52],"(Weil's":[55],"theorem).":[56],"I":[57],"restrict":[58],"myself":[59],"here":[60],"to":[61],"showing":[62],"(Theorem":[63,89],"20)":[64],"how":[65],"one":[66],"find":[68],"large":[70],"\u201cdifferentially":[71],"chunk\u201d":[74],"inside":[75],"defined":[78],"field.":[83],"The":[84,122,222],"rest":[85],"21)":[90],"follows":[91],"routinely,":[92],"as":[93],"[B].":[95],"What":[96],"is,":[97],"perhaps,":[98],"interest":[100],"proof":[104],"proceeds":[105],"at":[106],"completely":[108],"general":[109],"(soft)":[110],"model":[111],"theoretic":[112],"level,":[113],"once":[114],"Facts":[115],"1\u20134":[116],"below":[117],"are":[118,188],"known.":[119],"Fact":[120,149,170,220],"1.":[121],"theory":[123,223],"complete":[132],"and":[133,185,187,218],"has":[134],"quantifier":[135],"elimination":[136],"language":[139],"differential":[141,166,183,213],"(+,":[143],"\u00b7,0,1,":[144],"\u22121":[145],",":[146],"d":[147],").":[148,219],"2.":[150],"Affine":[151],"n-space":[152],"Noetherian":[160],"space":[161],"when":[162],"Zariski":[167],"topology":[168],"3.":[171],"If":[172],"field,":[178,184],"k":[179,199,208,217],"\u2286":[180],"k,":[190],"then":[191],"closure":[197],"\u25e1":[200],"iff":[201],"\u2208":[203],"\u2039":[204,209],"\u203a":[205,210],"(":[206],"where":[207],"denotes":[211],"generated":[215],"by":[216],"4.":[221],"zero":[230],"totally":[232],"transcendental":[233],"(in":[234],"particular,":[235],"stable":[236],")":[237]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}