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Orice numar natural este dimensiune omologica

 
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Cristi Popa
Euclid


Joined: 10 Nov 2007
Posts: 38
Location: Paris

PostPosted: Sat Jan 15, 2011 1:10 pm    Post subject: Orice numar natural este dimensiune omologica Reply with quote

Oricare ar fi numarul natural n exista un modul a carui dimensiune proiectiva sa fie n. Analog, pentru dimensiunile injectiva si plata.
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Dragos Fratila
Newton


Joined: 04 Oct 2007
Posts: 335
Location: Paris

PostPosted: Sun Jan 16, 2011 1:35 am    Post subject: Reply with quote

Poti de fapt sa ceri putin mai mult: pentru fiecare nr. natural exista inel care are dimengiunea globala n. Asta implica automat ca are module de dim. omologica n.

Un exemplu simplu e orice inel local al unui punct nesingular al unei varietati de dimensiune n. De exemplu, uitandu-ne la spatiul afin n-dimensional, \mathbb{C}[X_1,...,X_n]_{(X_1,...,X_n)} are dimensiune globala n.

Legatura intre dimensiunea globala si regularitatea unui inel e data de o teorema a lui Serre
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Cristi Popa
Euclid


Joined: 10 Nov 2007
Posts: 38
Location: Paris

PostPosted: Sun Jan 16, 2011 10:24 am    Post subject: Reply with quote

Aceasta era si solutia mea, folosind teorema Auslander-Buchsbaum-Serre.
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