{"id":"https://openalex.org/W1996041285","doi":"https://doi.org/10.1007/s000170050029","title":"From Numbers to Rings: The Early History of Ring Theory","display_name":"From Numbers to Rings: The Early History of Ring Theory","publication_year":1998,"publication_date":"1998-03-31","ids":{"openalex":"https://openalex.org/W1996041285","doi":"https://doi.org/10.1007/s000170050029","mag":"1996041285"},"language":"en","primary_location":{"id":"doi:10.1007/s000170050029","doi":"https://doi.org/10.1007/s000170050029","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s000170050029","pdf_url":"http://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=53&iss=1&rank=2","source":{"id":"https://openalex.org/S4210222070","display_name":"Elemente der Mathematik","issn_l":"0013-6018","issn":["0013-6018","1420-8962"],"is_oa":false,"is_in_doaj":true,"is_core":false,"listed_in":["anvur-scientific","doaj","dongbi-c","jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310316982","host_organization_name":"European Mathematical Society","host_organization_lineage":["https://openalex.org/P4310316982"],"host_organization_lineage_names":["European Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Elemente der Mathematik","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=53&iss=1&rank=2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070367146","display_name":"Israel Kleiner","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]},{"id":"https://openalex.org/I4210112962","display_name":"York University","ror":"https://ror.org/022jz8688","country_code":"US","type":"education","lineage":["https://openalex.org/I4210112962"]}],"countries":["CA","US"],"is_corresponding":true,"raw_author_name":"Israel Kleiner","raw_affiliation_strings":["York University, Toronto, Canada","Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3 kleiner@yorku.ca"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"York University, Toronto, Canada","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, York University, North York, Ontario, Canada M3J 1P3 kleiner@yorku.ca","institution_ids":["https://openalex.org/I192455969","https://openalex.org/I4210112962"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070367146"],"corresponding_institution_ids":["https://openalex.org/I192455969","https://openalex.org/I4210112962"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.26803395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"53","issue":"1","first_page":"18","last_page":"35"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.6826000213623047,"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"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.6826000213623047,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.2653999924659729,"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":0.012900000438094139,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/commutative-algebra","display_name":"commutative algebra","score":0.8830000162124634},{"id":"https://openalex.org/keywords/noncommutative-ring-theory","display_name":"noncommutative ring theory","score":0.996999979019165},{"id":"https://openalex.org/keywords/algebraic-number-theory","display_name":"algebraic number theory","score":0.8080000281333923},{"id":"https://openalex.org/keywords/algebraic-function-fields","display_name":"algebraic function fields","score":0.8519999980926514},{"id":"https://openalex.org/keywords/ring-of-integers","display_name":"ring of integers","score":0.8180000185966492},{"id":"https://openalex.org/keywords/invariant-theory","display_name":"invariant theory","score":0.7689999938011169},{"id":"https://openalex.org/keywords/algebraic-geometry","display_name":"algebraic geometry","score":0.7590000033378601}],"concepts":[{"id":"https://openalex.org/C196434610","wikidata":"https://www.wikidata.org/wiki/Q1208658","display_name":"Ring theory","level":4,"score":0.9036349058151245},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.8925285339355469},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.765609622001648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7206015586853027},{"id":"https://openalex.org/C125225535","wikidata":"https://www.wikidata.org/wiki/Q7049224","display_name":"Noncommutative ring","level":3,"score":0.7007250189781189},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.6302227973937988},{"id":"https://openalex.org/C78313660","wikidata":"https://www.wikidata.org/wiki/Q727659","display_name":"Commutative algebra","level":2,"score":0.6255252361297607},{"id":"https://openalex.org/C185382297","wikidata":"https://www.wikidata.org/wiki/Q16959942","display_name":"Derived algebraic geometry","level":5,"score":0.6243121027946472},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.622456431388855},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.6099623441696167},{"id":"https://openalex.org/C142109727","wikidata":"https://www.wikidata.org/wiki/Q1142704","display_name":"Local ring","level":3,"score":0.5463460683822632},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5141275525093079},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5132777690887451},{"id":"https://openalex.org/C193645952","wikidata":"https://www.wikidata.org/wiki/Q7049219","display_name":"Noncommutative algebraic geometry","level":4,"score":0.5078805088996887},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5016894340515137},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43140709400177},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.4187451899051666},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.3962874412536621},{"id":"https://openalex.org/C29384965","wikidata":"https://www.wikidata.org/wiki/Q7049223","display_name":"Noncommutative quantum field theory","level":3,"score":0.24531129002571106},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10168677568435669},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09879651665687561},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.0648004412651062},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"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},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s000170050029","doi":"https://doi.org/10.1007/s000170050029","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s000170050029","pdf_url":"http://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=53&iss=1&rank=2","source":{"id":"https://openalex.org/S4210222070","display_name":"Elemente der Mathematik","issn_l":"0013-6018","issn":["0013-6018","1420-8962"],"is_oa":false,"is_in_doaj":true,"is_core":false,"listed_in":["anvur-scientific","doaj","dongbi-c","jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310316982","host_organization_name":"European Mathematical Society","host_organization_lineage":["https://openalex.org/P4310316982"],"host_organization_lineage_names":["European Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Elemente der Mathematik","raw_type":"journal-article"},{"id":"doi:10.5169/seals-3627","doi":"https://doi.org/10.5169/seals-3627","is_oa":true,"landing_page_url":"https://doi.org/10.5169/seals-3627","pdf_url":null,"source":{"id":"https://openalex.org/S7407051277","display_name":"E-Periodica","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s000170050029","doi":"https://doi.org/10.1007/s000170050029","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s000170050029","pdf_url":"http://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=53&iss=1&rank=2","source":{"id":"https://openalex.org/S4210222070","display_name":"Elemente der Mathematik","issn_l":"0013-6018","issn":["0013-6018","1420-8962"],"is_oa":false,"is_in_doaj":true,"is_core":false,"listed_in":["anvur-scientific","doaj","dongbi-c","jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310316982","host_organization_name":"European Mathematical Society","host_organization_lineage":["https://openalex.org/P4310316982"],"host_organization_lineage_names":["European Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Elemente der Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1996041285.pdf","grobid_xml":"https://content.openalex.org/works/W1996041285.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W639706555","https://openalex.org/W1495410784","https://openalex.org/W1519565561","https://openalex.org/W1548377147","https://openalex.org/W1568297638","https://openalex.org/W1573740894","https://openalex.org/W1592261758","https://openalex.org/W1604636366","https://openalex.org/W1977852626","https://openalex.org/W1982469370","https://openalex.org/W1984881413","https://openalex.org/W1999680025","https://openalex.org/W2095443798","https://openalex.org/W2111560250","https://openalex.org/W2319466955","https://openalex.org/W2573667097","https://openalex.org/W2796914266","https://openalex.org/W3026048605","https://openalex.org/W3217725329","https://openalex.org/W4234426551","https://openalex.org/W4292482156","https://openalex.org/W4388436028","https://openalex.org/W6649967308","https://openalex.org/W6823989192"],"related_works":["https://openalex.org/W1524935011","https://openalex.org/W4361793526","https://openalex.org/W4248827262","https://openalex.org/W594662916","https://openalex.org/W2517558352","https://openalex.org/W2052213745","https://openalex.org/W808277865","https://openalex.org/W4307280421","https://openalex.org/W4224326930","https://openalex.org/W2127315228"],"abstract_inverted_index":{"Rings":[0],"fall":[1],"into":[2],"two":[3,14,64],"broad":[4],"categories:":[5],"commutative":[6],"and":[7,20,35,54,58],"noncommutative.":[8],"The":[9],"abstract":[10],"theories":[11],"of":[12,42,48,61],"these":[13,43],"categories":[15],"came":[16],"from":[17],"distinct":[18],"sources":[19],"developed":[21],"in":[22,29,50,63],"different":[23],"directions.":[24],"Commutative":[25],"ring":[26,69],"theory":[27,70],"originated":[28],"algebraic":[30,33,51,55],"number":[31,52],"theory,":[32],"geometry,":[34],"invariant":[36],"theory.":[37],"Central":[38],"to":[39],"the":[40,46,59],"development":[41],"subjects":[44],"were":[45],"rings":[47,60],"integers":[49],"fields":[53],"function":[56],"fields,":[57],"polynomials":[62],"or":[65],"more":[66],"variables.":[67],"Noncommutative":[68],"began":[71],"with":[72],"attempts":[73],".":[74]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}