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?