{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T16:45:24Z","timestamp":1648917924184},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6859,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1995,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study first-order properties of the quotient rings <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018582_inline1\" \/>(<jats:italic>V<\/jats:italic>)\/<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018582_inline2\" \/> by a prime ideal <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018582_inline2\" \/> where <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200018582_inline1\" \/>(<jats:italic>V<\/jats:italic>) is the ring of <jats:italic>p<\/jats:italic>-adic valued continuous definable functions on some affine <jats:italic>p<\/jats:italic>-adic variety <jats:italic>V<\/jats:italic>. We show that they are integrally closed Henselian local rings, with a <jats:italic>p<\/jats:italic>-adically closed residue field and field of fractions, and they are not valuation rings in general but always satisfy \u2200 <jats:italic>x, y<\/jats:italic>(<jats:italic>x<\/jats:italic>\u2223<jats:italic>y<\/jats:italic><jats:sup>2<\/jats:sup> \u2228 <jats:italic>y<\/jats:italic>\u2223<jats:italic>x<\/jats:italic><jats:sup>2<\/jats:sup>).<\/jats:p>","DOI":"10.2307\/2275843","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:55:05Z","timestamp":1146956105000},"page":"484-497","source":"Crossref","is-referenced-by-count":4,"title":["Anneaux de fonctions <i>p<\/i>-adiques"],"prefix":"10.1017","volume":"60","author":[{"given":"Luc","family":"B\u00e9lair","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200018582_ref011","first-page":"154","article-title":"p-adic semi-algebraic sets and cell decomposition","volume":"369","author":"Denef","year":"1986","journal-title":"Jounal f\u00fcr Reine und Angewandte Mathematik"},{"key":"S0022481200018582_ref004","volume-title":"G\u00e9om\u00e9trie alg\u00e9brique r\u00e9elle","author":"Bochnak","year":"1987"},{"key":"S0022481200018582_ref017","first-page":"1165","volume":"53","author":"Pillay","year":"1988","journal-title":"Sheaves of continuous definable functions"},{"key":"S0022481200018582_ref016","unstructured":"[Ha] Haskell D. , Topics in constructive p-adic algebra, Ph.D. thesis, Stanford University, Stanford, California, 1990."},{"key":"S0022481200018582_ref005","volume-title":"On the L-adic spectrum","volume":"40","author":"Br\u00f6cker","year":"1986"},{"key":"S0022481200018582_ref001","volume-title":"Les nombres p-adiques","author":"Amice","year":"1975"},{"key":"S0022481200018582_ref002","first-page":"539","volume":"56","author":"B\u00e9lair","year":"1991","journal-title":"Anneaux p-adiquement clos et anneaux de fonctions d\u00e9finissables"},{"key":"S0022481200018582_ref006","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511721533"},{"key":"S0022481200018582_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(83)90058-0"},{"key":"S0022481200018582_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90019-2"},{"key":"S0022481200018582_ref009","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/008\/653174"},{"key":"S0022481200018582_ref012","unstructured":"[D1] Dickmann M. , A property of the continuous semialgebraic functions defined on a real curve, manuscrit."},{"key":"S0022481200018582_ref013","first-page":"76","volume-title":"Methods in Mathematical logic, Proceedings, Caracas, 1983","volume":"1130","author":"Dickmann","year":"1985"},{"key":"S0022481200018582_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-7819-2"},{"key":"S0022481200018582_ref019","first-page":"1138","volume":"53","author":"Scowcroft","year":"1988","journal-title":"On the structure of semialgebraic set over p-adic fields"},{"key":"S0022481200018582_ref014","unstructured":"[D3] Dickmann M. , Applications of model theory to real algebraic geometry (\u00e0 para\u00eetre)."},{"key":"S0022481200018582_ref018","first-page":"175","volume-title":"Algebra and order: proceedings of the first international symposium on ordered algebraic structures, Luminy-Marseille, 1984","author":"Schwartz","year":"1986"},{"key":"S0022481200018582_ref020","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90061-4"},{"key":"S0022481200018582_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(88)90043-7"},{"key":"S0022481200018582_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389133"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200018582","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,13]],"date-time":"2019-05-13T21:52:50Z","timestamp":1557784370000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200018582\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":20,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["S0022481200018582"],"URL":"https:\/\/doi.org\/10.2307\/2275843","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}