Once again, we let X be the closure of U in
An, and let
Y be the closure of
(U) in
An-1. Finally,
let Z = X - U. Study the
ideals I(X) and I(Z), using methods similar to
those used in part b. It may help to work modulo I(Y),
thus making it possible to consider ideals in A(Y)[t],
where t is an indeterminate. After adjoining inverses of
suitable elements of A(Y), we can even assume that these
ideals are principal!
The most challenging case is where
(Z) is dense
in Y. Study the discussion at the bottom of page 40 of the text
to see whether this situation leads to a contradiction. (Calculation
of a resultant may or may not be an essential feature ... )
Back to the exercises
Comments and inquiries to: roberts@math.umn.edu
Back to my homepage: http://www.math.umn.edu/~roberts