{"id":1420,"date":"2022-11-20T14:31:51","date_gmt":"2022-11-20T14:31:51","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=1420"},"modified":"2022-12-05T22:05:35","modified_gmt":"2022-12-05T22:05:35","slug":"s-quasi-modular-closure-of-a-finite-purely-inseparable-extension","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/s-quasi-modular-closure-of-a-finite-purely-inseparable-extension\/","title":{"rendered":"s-quasi-modular closure of a finite purely inseparable extension"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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s-quasi-modular closure of a finite purely inseparable extension<\/strong><\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n

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El Hassane Fliouet <\/strong><\/i>
Regional Center for the Professions of Education and Training, Agadir, Morocco<\/p>\n\n\n\n

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Pages 418-427 | Received 10 August 2022, Accepted 31 October 2022, Published 06 December 2022 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

Given a field k of characteristic p\\neq 0<\/span>. Let K \/k<\/span> be a finite purely inseparable field extension of j-th exponent e_j<\/span>. Recall that K<\/span> is modular over k<\/span> if and only if for any n \\in \\mathbb{N}<\/span>, K^{p^n}<\/span> and k<\/span> are linearly disjoint over K^{p^n} \\cap k<\/span>. This notion, which plays a central role in the development of the Galois theory relating to purely inseparable extensions, was used by M. E. Sweedler to characterize purely inseparable extensions of bounded exponent which were tensor products of simple extensions. Since then, many authors have studied various properties of modular field extensions, including the existence of modular closures. Similarly, K \/k<\/span> is said to be s-quasi-modular if for all i \\in \\{1,\u2026, e_s\\}<\/span>, K^{p^i}<\/span> and k<\/span> are K^{p^i} \\cap k<\/span> linearly disjoint. Motivated by R. Rasala\u2019s work, We characterize the notion of s-quasi modularity and we then a method which makes it possible to build the s-quasi modular closure of K \/k<\/span>. In particular, if s = n<\/span>, we find the Rasala result.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  Purely inseparable extension, modular extension, s-quasi-modular.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 12F15.<\/p>\n\n\n\n

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0102MJAGA418_427<\/a>\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles s-quasi-modular closure of a finite purely inseparable extension El Hassane Fliouet Regional Center for the Professions of Education and Training, Agadir, Morocco Pages 418-427 | Received 10 August 2022, Accepted 31 October 2022, Published 06 December 2022 Abstract Given a field k of characteristic . Let Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-1420","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=1420"}],"version-history":[{"count":9,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1420\/revisions"}],"predecessor-version":[{"id":1557,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/1420\/revisions\/1557"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=1420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}