{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T19:31:16Z","timestamp":1769196676065,"version":"3.49.0"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":7681,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1993,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>One of the main theorems of the paper states the following. Let <jats:italic>R-K-M<\/jats:italic> be finite extensions of a rational one variable function field <jats:italic>R<\/jats:italic> over a finite field of constants. Let <jats:italic>S<\/jats:italic> be a finite set of valuations of <jats:italic>K<\/jats:italic>. Then the ring of elements of <jats:italic>K<\/jats:italic> having no poles outside <jats:italic>S<\/jats:italic> has a Diophantine definition over its integral closure in <jats:italic>M<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2275331","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:47:31Z","timestamp":1146955651000},"page":"158-192","source":"Crossref","is-referenced-by-count":7,"title":["Diophantine relations between rings of <i>S<\/i>-integers of fields of algebraic functions in one variable over constant fields of positive characteristic"],"prefix":"10.1017","volume":"58","author":[{"given":"Alexandra","family":"Shlapentokh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200021708_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420703"},{"key":"S0022481200021708_ref012","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-18.3.385"},{"key":"S0022481200021708_ref004","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420805"},{"key":"S0022481200021708_ref011","first-page":"214","article-title":"Hilbert's tenth problem for quadratic rings","volume":"48","author":"Denef","year":"1975","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200021708_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1980-0549163-X"},{"key":"S0022481200021708_ref005","first-page":"275","article-title":"Hilbert's tenth problem for rings of algebraic functions of positive characteristic","volume":"333","author":"Shlapentokh","year":"1992","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200021708_ref008","volume-title":"Algebraic number theory","author":"Lang","year":"1970"},{"key":"S0022481200021708_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-07216-5"},{"key":"S0022481200021708_ref001","first-page":"323","volume-title":"Positive aspects of a negatives solution","volume":"28","author":"Davis","year":"1976"},{"key":"S0022481200021708_ref009","volume-title":"Algebra","author":"Lang","year":"1971"},{"key":"S0022481200021708_ref006","volume-title":"Algebraic numbers and algebraic functions","author":"Artin","year":"1967"},{"key":"S0022481200021708_ref014","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160430807"},{"key":"S0022481200021708_ref016","article-title":"Diophantine unsolvability for function fields over certain infinite fields of characteristic P","author":"Kim","journal-title":"Journal of Algebra"},{"key":"S0022481200021708_ref013","first-page":"131","volume-title":"Logic Colloquium 78","author":"Denef","year":"1979"},{"key":"S0022481200021708_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF01239506"},{"key":"S0022481200021708_ref002","first-page":"611","article-title":"Hilbert's tenth problem for a class of rings of algebraic integers","volume":"10","author":"Pheidas","year":"1988","journal-title":"Proceedings of the American Mathematical Society"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200021708","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T19:14:44Z","timestamp":1558034084000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200021708\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,3]]}},"alternative-id":["S0022481200021708"],"URL":"https:\/\/doi.org\/10.2307\/2275331","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}