{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,3]],"date-time":"2023-05-03T06:11:06Z","timestamp":1683094266546},"reference-count":8,"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":9415,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1988,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Baur a d\u00e9fini la notion d'extension s\u00e9par\u00e9e de corps valu\u00e9s et montr\u00e9 que toute extension d'un corps maximal est s\u00e9par\u00e9e. Nous prouvons que, si (<jats:italic>K<\/jats:italic>, \u03c5) est henselien et de caract\u00e9ristique r\u00e9siduelle nulle, alors (<jats:italic>K<\/jats:italic>, \u03c5) \u2282 (<jats:italic>L, w<\/jats:italic>) est s\u00e9par\u00e9e ssi <jats:italic>L<\/jats:italic> est lin\u00e9airement disjoint sur <jats:italic>K<\/jats:italic> de toute extension imm\u00e9diate de <jats:italic>K<\/jats:italic>.<\/jats:p><jats:p><jats:italic>Separated and immediate extensions of valued fields<\/jats:italic>. The notion of separated extension of valued fields was introduced by Baur. He showed that extensions of maximal fields are separated. We prove that, when (<jats:italic>K<\/jats:italic>, \u03c5) is Henselian with residual characteristic 0, then (<jats:italic>K<\/jats:italic>, \u03c5) \u2282 (<jats:italic>L, w<\/jats:italic>) is separated iff <jats:italic>L<\/jats:italic> is linearly disjoint over <jats:italic>K<\/jats:italic> from each immediate extension of <jats:italic>K<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s002248120002836x","type":"journal-article","created":{"date-parts":[[2014,3,13]],"date-time":"2014-03-13T12:48:53Z","timestamp":1394714933000},"page":"421-428","source":"Crossref","is-referenced-by-count":0,"title":["Extensions s\u00e9par\u00e9es et imm\u00e9diates de corps valu\u00e9s"],"prefix":"10.1017","volume":"53","author":[{"given":"Fran\u00e7oise","family":"Delon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120002836X_ref002","first-page":"669","volume":"47","author":"Baur","year":"1982","journal-title":"On the theory of pairs of real closed fields. II"},{"key":"S002248120002836X_ref005","volume-title":"Defectless extensions of valued fields","author":"Kuhlmann","year":"1987"},{"key":"S002248120002836X_ref007","unstructured":"Leloup G. , Th\u00e9ories compl\u00e8tes de corps valu\u00e9s henseliens, Th\u00e8se de 3\u00e8me cycle, Universit\u00e9 Paris-VII, Paris, 1985."},{"key":"S002248120002836X_ref003","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S002248120002836X_ref004","unstructured":"Delon F. , Quelques propri\u00e9t\u00e9s des corps valu\u00e9s en th\u00e9orie des mod\u00e8les, Th\u00e8se de doctorat d'\u00e9tat, Universit\u00e9 Paris-VII, Paris, 1982."},{"key":"S002248120002836X_ref006","volume-title":"Introduction to algebraic geometry","author":"Lang","year":"1958"},{"key":"S002248120002836X_ref008","volume-title":"Th\u00e9orie des valuations","author":"Ribenboim","year":"1964"},{"key":"S002248120002836X_ref001","first-page":"25","volume-title":"Logic and algorithmic (in honour of E. Specker)","author":"Baur","year":"1982"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120002836X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,3]],"date-time":"2023-05-03T05:50:00Z","timestamp":1683093000000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120002836X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1988,6]]}},"alternative-id":["S002248120002836X"],"URL":"https:\/\/doi.org\/10.1017\/s002248120002836x","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,6]]}}}