{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:00:43Z","timestamp":1758279643664},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4210,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider separably closed fields of characteristic <jats:italic>p<\/jats:italic> &gt; 0 and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the <jats:italic>p<\/jats:italic>-component functions.<\/jats:p>","DOI":"10.2178\/jsl\/1190150144","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:14:26Z","timestamp":1197555266000},"page":"997-1015","source":"Crossref","is-referenced-by-count":5,"title":["The theory of modules of separably closed fields 1"],"prefix":"10.1017","volume":"67","author":[{"given":"Pilar","family":"Dellunde","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7oise","family":"Delon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7oise","family":"Point","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009373_ref003","unstructured":"Dellunde P. , Delon F. , and Point F. , The theory of modules of separably closed fields-2, preprint."},{"key":"S0022481200009373_ref011","first-page":"412","volume":"44","author":"Wood","year":"1979","journal-title":"Notes on the stability of separably closed fields"},{"key":"S0022481200009373_ref001","volume-title":"Sous-groupes infiniment d\u00e9finissables du groupe additif d'un corps s\u00e9parablement clos","author":"Blossier","year":"2001"},{"key":"S0022481200009373_ref004","first-page":"116","volume-title":"Suppl\u00e9ment au Bulletin de la Soci\u00e9t\u00e9 Math\u00e9matique de France","author":"Delon","year":"1988"},{"key":"S0022481200009373_ref005","first-page":"19","article-title":"Fields with a solvable theory","volume":"174","author":"Ershov","year":"1967","journal-title":"Doklady"},{"key":"S0022481200009373_ref006","volume-title":"Basic algebra I","author":"Jacobson","year":"1985"},{"key":"S0022481200009373_ref007","first-page":"188","volume":"53","author":"Martin","year":"1988","journal-title":"Definability in reducts of algebraically closed fields"},{"key":"S0022481200009373_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1933-1501703-0"},{"key":"S0022481200009373_ref010","volume-title":"London Mathematical Society Lecture Notes Series","volume":"130","author":"Prest","year":"1988"},{"key":"S0022481200009373_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(84)90014-9"},{"key":"S0022481200009373_ref002","volume-title":"Encyclopedia of mathematics and its applications","volume":"57","author":"Cohn","year":"1995"},{"key":"S0022481200009373_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1968173"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009373","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T20:45:23Z","timestamp":1557175523000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009373\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["S0022481200009373"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150144","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}