Timeline for Depth of intersection

8 events

when toggle format	what		by	license	comment
S Jul 23, 2013 at 22:18	history	suggested	user26857	CC BY-SA 3.0	Edited by texifing.
Jul 23, 2013 at 21:56	review	Suggested edits
S Jul 23, 2013 at 22:18
Oct 12, 2011 at 5:54	comment	added	Thomas Kahle		A relation between $\text{depth} I$ and $\text{depth} I \cap K[x_1,\dots,x_r]$ can hardly exist. If $r=n/2$, say, then $I=(x_1,\dots,x_r)$ and $I' = (x_{r+1}, \dots, x_n)$ are two ideals, both containing a regular sequence of length $r$. In the first case the entire regular sequence survives, in the second case nothing of it survives.
Jun 14, 2011 at 20:30	comment	added	Andrei		I think that if we note $J=(x_{r+1},...,x_n)$ then $ I \cap K[x_1,...,x_r] = \frac{I+J}{J}$ and then we get depth $(I \cap K[x_1,...,x_r])$ from depth lemma. In general for $M \cap N$ I don't see anything.
Jun 14, 2011 at 14:06	comment	added	Andrei		and yes I mean depth$_S I$, at least that's the notation I know.
Jun 14, 2011 at 14:01	comment	added	Andrei		en.wikipedia.org/wiki/Depth_%28ring_theory%29 this is the definition for depth
Jun 14, 2011 at 12:48	comment	added	Sándor Kovács		What do you mean by "depth"? That is usually associated to an ideal where the elements are taken from. Or do you mean the grade? For an ideal that is actually $\mathrm{depth}_I(S)$. Is that what you mean?
Jun 13, 2011 at 21:57	history	asked	Andrei	CC BY-SA 3.0