{"id":457,"date":"2025-07-17T09:44:46","date_gmt":"2025-07-17T08:44:46","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=457"},"modified":"2025-07-18T09:35:17","modified_gmt":"2025-07-18T08:35:17","slug":"inclusions-de-rang-estable-1","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/inclusions-de-rang-estable-1\/","title":{"rendered":"Inclusions de rang estable 1"},"content":{"rendered":"\n<p>El rang estable \u00e9s una propietat introdu\u00efda per Bass els anys 60, i que es pot pensar com una noci\u00f3 no commutativa de dimensi\u00f3. En efecte, Vaserstein va provar que per anells de funcions cont\u00ednues a valors complexos \\(C(X)\\), el rang estable \u00e9s essencialment la meitat de la part entera de la dimensi\u00f3 de \\(X\\). El valor m\u00e9s baix del rang estable est\u00e0 estretament relacionat, entre altres, amb el c\u00e0lcul del primer grup de teoria K, aix\u00ed com amb propietats de cancel\u00b7laci\u00f3 de m\u00f2duls. Per C*-\u00e0lgebres, la noci\u00f3 de rang estable \\(1\\) est\u00e0 sent fonamental en l&#8217;estudi de l&#8217;estructura i la classificaci\u00f3 d&#8217;aquests objectes, i es pot formular dient que el conjunt d&#8217;elements invertibles \u00e9s dens a l&#8217;\u00e1lgebra (en la topologia de la norma). Despr\u00e9s d&#8217;una introducci\u00f3 a la teoria b\u00e0sica necess\u00e0ria, el treball buscar\u00e0 estendre (per a anells i, en la mesura del possible, tamb\u00e9 per C*-\u00e0lgebres) aquest concepte a inclusions d&#8217;anells \\(R\\subseteq S\\) que comparteixen unitat, tot intentant establir propietats similars a les ja conegudes en el cas que \\(R=S\\).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>El rang estable \u00e9s una propietat introdu\u00efda per Bass els anys 60, i que es pot pensar com una noci\u00f3 no commutativa de dimensi\u00f3. En efecte, Vaserstein va provar que per anells de funcions cont\u00ednues a valors complexos \\(C(X)\\), el rang estable \u00e9s essencialment la meitat de la part entera de la dimensi\u00f3 de \\(X\\). [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28,29],"tags":[46],"class_list":["post-457","post","type-post","status-publish","format-standard","hentry","category-algebra","category-analisi-matematica","tag-francesc-perera"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/457","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=457"}],"version-history":[{"count":3,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/457\/revisions"}],"predecessor-version":[{"id":460,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/457\/revisions\/460"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=457"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=457"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=457"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}