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Edited by texifing.
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edit approved Jul 23, 2013 at 22:18
user26857
edit approved Jul 23, 2013 at 22:18
user26857
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depth Depth of intersection

Hi letLet $I$ be an ideal in $S=K[x_1,...,x_n]$$S=K[x_1,\dots,x_n]$. Can we compute depth $( I \cap K[x_1,...,x_r])$$\operatorname{depth}(I\cap K[x_1,\dots,x_r])$ with $r \leq n$ ?? Is there any relation between depth $I$ and depth $( I \cap K[x_1,...,x_r])$ ?$\operatorname{depth}(I\cap K[x_1,\dots,x_r])$?

And what cacan we tell about depth $(M \cap N)$$\operatorname{depth}(M \cap N)$ when M,N$M,N$ are S $S$- modules modules? Does it have any bounds?

depth of intersection

Hi let $I$ be an ideal in $S=K[x_1,...,x_n]$. Can we compute depth $( I \cap K[x_1,...,x_r])$ with $r \leq n$ ?? Is there any relation between depth $I$ and depth $( I \cap K[x_1,...,x_r])$ ??

And what ca we tell about depth $(M \cap N)$ when M,N are S - modules ? Does it have any bounds?

Depth of intersection

Let $I$ be an ideal in $S=K[x_1,\dots,x_n]$. Can we compute $\operatorname{depth}(I\cap K[x_1,\dots,x_r])$ with $r \leq n$? Is there any relation between depth $I$ and $\operatorname{depth}(I\cap K[x_1,\dots,x_r])$?

And what can we tell about $\operatorname{depth}(M \cap N)$ when $M,N$ are $S$-modules? Does it have any bounds?

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Andrei
Andrei
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depth of intersection

Hi let $I$ be an ideal in $S=K[x_1,...,x_n]$. Can we compute depth $( I \cap K[x_1,...,x_r])$ with $r \leq n$ ?? Is there any relation between depth $I$ and depth $( I \cap K[x_1,...,x_r])$ ??

And what ca we tell about depth $(M \cap N)$ when M,N are S - modules ? Does it have any bounds?