Math 724
Fall 2001
Homework 4
- Let
be a Dedekind
domain. Show that any ideal of
may be generated
by at most two elements.
- Let
be
one-dimensional and Noetherian.
a)
Show
that the integral closure of
is Dedekind.
b)
Show
that if
is local, then the
integral closure of
is a PID with only
finitely many primes.
- Let
be a domain and
a prime ideal
such that
Show that
is a Noetherian
valuation domain.
- Give an example of a
domain
with quotient
field
and an overring
with
or show that no
such example can exist.