Timeline for Comparation of dimensions of rings

10 events

when toggle format	what		by	license	comment
May 19, 2011 at 9:32	vote	accept	Li Zhan
May 19, 2011 at 9:19	vote	accept	Li Zhan
May 19, 2011 at 9:32
May 19, 2011 at 3:42	comment	added	Li Zhan		Dear Konstantin Ardakov，could you say more about how to apply Noether Normalization to $B$ to get $p$ generated by $dim(B_p)$ elements? After konwing this, it will be perfect for applying Krull's theorem, because taking into account the minimality of $q$ , one can prove prime ideal $qA_q$ is just minimal over $pA_q$ .
May 19, 2011 at 3:03	comment	added	Li Zhan		Dear Karl Schwede, thank you! The direction you point out used to make me unease when translate it into algebra facts.
May 18, 2011 at 16:12	comment	added	Karl Schwede		That should have read "Exercise 21(v) in the first chapter of Atiyah-Macdonald".
May 18, 2011 at 14:14	comment	added	Karl Schwede		A map of finitely generated $k$-algebra domains $B \to A$, induces a dominant map $f:\text{Spec} A \to \text{Spec} B$ if and only if $B \to A$ is injective. For the direction you are confused about (injective => dominant) see Exercise 21(v) in Atiyah-Macdonald.
May 18, 2011 at 14:09	answer	added	Georges Elencwajg		timeline score: 5
May 18, 2011 at 9:43	comment	added	user91132		Try using Noether Normalization on $B$ to get $p$ generated by $dim B_p$ elements, and then perhaps try to apply Krull's Hauptidealsatz to $pA_q$.
May 18, 2011 at 8:28	history	edited	Li Zhan	CC BY-SA 3.0	added 29 characters in body
May 18, 2011 at 8:12	history	asked	Li Zhan	CC BY-SA 3.0