# Nonunique factorization theory

1. Dec 13, 2011

### camilus

Im applying to an REU in San Diego State where the focus will be Nonunique factorization theory but I'm clueless as to what this actually is. Does anybody know anything about this?

2. Dec 14, 2011

### Mooky

I know nothing about this, but brush up of your knowledge of basic number theory, including primes and factorizations, and you should be fine. This is an REU, so they don't expect you do be an expert, especially on a relatively obscure field such as this. It sounds very interesting. Enjoy!

3. Dec 14, 2011

### Mathguy15

I have heard of a construction that gives a set of integers that cannot be factorized uniquely. Consider the numbers that have an even number of distinct primes as factors. It is not hard to see that the primes of this set are those integers that have at most two distinct prime factors. Let p and q be two ordinary prime numbers. Then, p^2*q^2=(pq)^2. Since p^2, q^2, and pq have no factors in this set, p^2*q^2 is a counterexample to unique factorization in this set. I suspect that something similar may happen when an even number is replaced with multiples of any integer. Maybe something like this is what you were looking for? You might be looking for something a great deal more advanced. This is just what I've heard that might be related to what you want.

Um, something is happening. I am not reposting this. I think something's going wrong with my computer. I keep clicking edit and i get a new post. SORRY!

4. Dec 14, 2011

### Mathguy15

EDIT:SORRY, I did not carefully read your post. You are looking for something specifically about the REU. Sorry for my redundant ramblings.

5. Dec 14, 2011

### Mathguy15

SORRY, I did not carefully read your post. You are looking for something specifically about the REU. Sorry for my redundant ramblings.

edit:Sorry for the repost.

6. Dec 16, 2011

### lostcauses10x

do an internet search for Non Unique factorization. A lot of material is available out there.