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.