Math 793

Summer 2001

Homework 5

Turn in at least two by Thursday July 19, 2001.

1. Let be a nonzero prime and let be an elementary abelian group (that is ). Show that the Davenport constant of is given by

2. Give an example of an HFD that possesses an element with infinitely many distinct irreducible factorizations (hint: perhaps consider the ring where and are fields with some appropriate conditions).

3. (Adapted from a paper of S. Chapman and W. Smith). Let be a Dedekind domain with torsion class group and assume that every ideal class contains a prime ideal. Prove that the following conditions are equivalent:

a)

b) is an HFD.

c) is a HFD for some

d) is a CHFD for some