{"id":"https://openalex.org/W2151063322","doi":"https://doi.org/10.2307/2275331","title":"Diophantine relations between rings of <i>S</i>-integers of fields of algebraic functions in one variable over constant fields of positive characteristic","display_name":"Diophantine relations between rings of <i>S</i>-integers of fields of algebraic functions in one variable over constant fields of positive characteristic","publication_year":1993,"publication_date":"1993-03-01","ids":{"openalex":"https://openalex.org/W2151063322","doi":"https://doi.org/10.2307/2275331","mag":"2151063322"},"language":"en","primary_location":{"id":"doi:10.2307/2275331","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275331","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/A5020820702","display_name":"Alexandra Shlapentokh","orcid":"https://orcid.org/0000-0003-1990-909X"},"institutions":[{"id":"https://openalex.org/I186335123","display_name":"East Carolina University","ror":"https://ror.org/01vx35703","country_code":"US","type":"education","lineage":["https://openalex.org/I186335123"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexandra Shlapentokh","raw_affiliation_strings":["Department of Mathematics, East Carolina University, Greenville, North Carolina 27858, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, East Carolina University, Greenville, North Carolina 27858, E-mail:","institution_ids":["https://openalex.org/I186335123"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020820702"],"corresponding_institution_ids":["https://openalex.org/I186335123"],"apc_list":null,"apc_paid":null,"fwci":1.5307,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.83808214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"58","issue":"1","first_page":"158","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9976000189781189,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9976000189781189,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.993399977684021,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.8433163166046143},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7976647615432739},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.692184329032898},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.6821568012237549},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.6591112017631531},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6399571299552917},{"id":"https://openalex.org/keywords/function-field","display_name":"Function field","score":0.5979382991790771},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5367874503135681},{"id":"https://openalex.org/keywords/algebraic-closure","display_name":"Algebraic closure","score":0.5184154510498047},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5136072635650635},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.5102849006652832},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48673465847969055},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4793473184108734},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4637618064880371},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.44254615902900696},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3329501748085022},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33171653747558594},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.07558780908584595}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.8433163166046143},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7976647615432739},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.692184329032898},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.6821568012237549},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6591112017631531},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6399571299552917},{"id":"https://openalex.org/C2778795570","wikidata":"https://www.wikidata.org/wiki/Q5508772","display_name":"Function field","level":3,"score":0.5979382991790771},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5367874503135681},{"id":"https://openalex.org/C182327082","wikidata":"https://www.wikidata.org/wiki/Q428290","display_name":"Algebraic closure","level":5,"score":0.5184154510498047},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5136072635650635},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.5102849006652832},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48673465847969055},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4793473184108734},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4637618064880371},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.44254615902900696},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3329501748085022},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33171653747558594},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.07558780908584595},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2275331","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275331","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1518509928","https://openalex.org/W1978114483","https://openalex.org/W1985669819","https://openalex.org/W1994747442","https://openalex.org/W1996875474","https://openalex.org/W1997264833","https://openalex.org/W2011938854","https://openalex.org/W2056133231","https://openalex.org/W2080000094","https://openalex.org/W2084867265","https://openalex.org/W2090472642","https://openalex.org/W2157736452","https://openalex.org/W2983337356","https://openalex.org/W3007836994","https://openalex.org/W4252597789","https://openalex.org/W6649330678","https://openalex.org/W6670598239","https://openalex.org/W6671742702"],"related_works":["https://openalex.org/W2020950773","https://openalex.org/W4300050005","https://openalex.org/W2479302379","https://openalex.org/W1995956684","https://openalex.org/W4287329661","https://openalex.org/W4360831352","https://openalex.org/W2161969647","https://openalex.org/W1986648786","https://openalex.org/W1823199905","https://openalex.org/W4296247563"],"abstract_inverted_index":{"Abstract":[0],"One":[1],"of":[2,6,17,29,37,39,45,47],"the":[3,7,10,43],"main":[4],"theorems":[5],"paper":[8],"states":[9],"following.":[11],"Let":[12,31],"R-K-M":[13],"be":[14,33],"finite":[15,27,35],"extensions":[16],"a":[18,26,34,55],"rational":[19],"one":[20],"variable":[21],"function":[22],"field":[23,28],"R":[24],"over":[25,58],"constants.":[30],"S":[32,53],"set":[36],"valuations":[38],"K":[40,48],".":[41,64],"Then":[42],"ring":[44],"elements":[46],"having":[49],"no":[50],"poles":[51],"outside":[52],"has":[54],"Diophantine":[56],"definition":[57],"its":[59],"integral":[60],"closure":[61],"in":[62],"M":[63]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}