{"id":90698,"date":"2018-03-11T10:09:14","date_gmt":"2018-03-11T10:09:14","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/la-categoria-de-modulos-firmes\/"},"modified":"2018-03-11T10:09:14","modified_gmt":"2018-03-11T10:09:14","slug":"la-categoria-de-modulos-firmes","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/teoria-de-categorias\/la-categoria-de-modulos-firmes\/","title":{"rendered":"La categor\u00eda de m\u00f3dulos firmes"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Juan  De La Cruz Gonz\u00e1lez F\u00e9rez <\/strong><\/h2>\n<p>Dado un anillo asociativo (no unitario) r, un m\u00f3dulo m sobre r se dice firme si es isomorfo de  forma can\u00f3nica al producto tensorial sobre r de r por m. La categor\u00eda formada por los m\u00f3dulos firmes es pues una generalizaci\u00f3n natural en el caso no unitario de las categor\u00edas de m\u00f3dulos unitarios para anillos con unidad, conservando casi todas las propiedades de \u00e9stas.   una propiedad fundamental y que permanec\u00eda como problema abierto era la abelianidad de la  categor\u00eda. En la memoria se prueba que en general la categor\u00eda no es abeliana mostrando un ejemplo de un anillo asociativo r y de un monomorfismo que no es n\u00facleo de ning\u00fan otro morfismo de la  categor\u00eda. Para llegar a este resultado, se realiza un estudio profundo de la categor\u00eda de  m\u00f3dulos firmes y de multitud de propiedades equivalentes a la abelianidad, as\u00ed como otras  en principio m\u00e1s d\u00e9biles y que tampoco se cumplen en general.  se prueba tambi\u00e9n que si la categor\u00eda de m\u00f3dulos firmes es abeliana, entonces los l\u00edmites directos son exactos y por lo tanto cumple la propiedad de ser grothendieck. Se estudian en detalle los l\u00edmites directos y se da un ejemplo de un anillo y de una familia de monomorfismos cuyo l\u00edmite no es un monomorfismo y por lo tanto los l\u00edmites directos no son exactos.  se estudian familias de anillos para los cuales la categor\u00eda de m\u00f3dulos firmes es abeliana, concretamente la clase de las \u00e1lgebras monomiales.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>La categor\u00eda de m\u00f3dulos firmes<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 La categor\u00eda de m\u00f3dulos firmes <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Juan  De La Cruz Gonz\u00e1lez F\u00e9rez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Murcia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 15\/12\/2008<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Leandro Marin Mu\u00f1oz<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jos\u00e9 Luis Gomez pardo <\/li>\n<li>nieves Rodriguez gonzalez (vocal)<\/li>\n<li>blas Torrecillas jover (vocal)<\/li>\n<li>Jos\u00e9 Luis Garcia hernandez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Juan De La Cruz Gonz\u00e1lez F\u00e9rez Dado un anillo asociativo (no unitario) r, un m\u00f3dulo m sobre [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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