{"id":4185,"date":"2021-09-17T09:48:23","date_gmt":"2021-09-17T08:48:23","guid":{"rendered":"https:\/\/cyberschool.univ-rennes.fr\/?page_id=4185"},"modified":"2026-03-12T14:30:53","modified_gmt":"2026-03-12T13:30:53","slug":"algebre-generale-de-base","status":"publish","type":"page","link":"https:\/\/cyberschool.univ-rennes.fr\/en\/education\/masters-and-postgraduate-programmes\/masters-in-mathematics-and-applications-it-mathematics-and-cryptography\/study-programme-of-the-masters-mathematics-and-applications-it-mathematics-and-cryptography\/algebre-generale-de-base\/","title":{"rendered":"Alg\u00e8bre g\u00e9n\u00e9rale de base"},"content":{"rendered":"\n<section class=\"txt\">\n    <div class=\"container\">\n        <div class=\"bloc-txt\">\n                            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Course description<\/h2>\n                        <div class=\"contain-txt\">\n<ul>\n<li>Modules sur un anneau.<\/li>\n<li>Alg\u00e8bre lin\u00e9aire : modules, sous-modules, quotients, familles libres, g\u00e9n\u00e9ratrices, bases. Cas des espaces vectoriels. R\u00e9seaux. Produit tensoriel de modules et d\u2019alg\u00e8bres (existence et propri\u00e9t\u00e9 universelle).<\/li>\n<li>Matrices. Op\u00e9rations \u00e9l\u00e9mentaires. Forme r\u00e9duite \u00e9chelonn\u00e9e par lignes (dans un corps), forme de Hermite (anneau euclidien) ; forme de Smith (anneau euclidien). Application aux groupes ab\u00e9liens de type fini et \u00e0 la r\u00e9duction des endomorphismes.<\/li>\n<li>Extensions de corps (\u00e9l\u00e9ments alg\u00e9briques, \u00e9l\u00e9ments transcendants d\u2019une extension), corps de rupture, de d\u00e9composition ; corps alg\u00e9briquement clos, existence d\u2019une cl\u00f4ture alg\u00e9brique.<\/li>\n<li>Corps finis (extensions de corps, corps finis, groupe multiplicatif d\u2019un corps fini), polyn\u00f4mes irr\u00e9ductibles sur un corps fini.<\/li>\n<\/ul>\n<\/div>\n\n        <\/div>\n    <\/div>\n<\/section>\n\n\n<section class=\"tuiles\">\n    <div class=\"container\">\n                <div class=\"bloc\">\n            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Skills to acquire<\/h2>\n            <p>Manipuler et appliquer les notions de base de l\u2019alg\u00e8bre.<\/p>\n\n                    <\/div>\n                <div class=\"bloc\">\n            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Keywords<\/h2>\n            <p>Modules, r\u00e9seaux, alg\u00e8bre lin\u00e9aire, extensions de corps, corps finis.<\/p>\n\n                    <\/div>\n            <\/div>\n<\/section>\n\n\n\n<section class=\"txt\">\n    <div class=\"container\">\n        <div class=\"bloc-txt\">\n                            <h2><span class=\"elipse\"><\/span><span class=\"trait\"><\/span>Biographies<\/h2>\n                        <div class=\"contain-txt\">\n<p><strong>Vincent Guirardel<\/strong> est professeur \u00e0 l\u2019Universit\u00e9 de Rennes, ancien membre de l\u2019Institut universitaire de France et directeur du Centre Henri Lebesgue.<\/p>\n<p><strong>Florent Ygouf<\/strong> est ma\u00eetre de conf\u00e9rences \u00e0 l\u2019Universit\u00e9 de Rennes.<\/p>\n<\/div>\n\n        <\/div>\n    <\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":8,"featured_media":0,"parent":11605,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.13 - 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