Non-unique Factorization Domain, but Factorization Domain.

Abstract

In this thesis, we study an integral domain which is not a unique factorization domain, but a factorization domain. We prove that an integral domain D=Z[√-p]={a+b√-p|a, b∈ Z}, for a prime , is not a unique factorization domain, but a factorization domain. Furthermore, we make some examples of an integral domain D=Z[√-p] and an integral domain D=Z[√2p] which are factorization domains, but not unique factorization domains.|이 논문에서는 factorization domain이지만, unique factorization domain이 아닌 integral domain에 대해 연구하였다. 소수 p에 대해 integral domain인 D=Z[√-p]={a+b√-p|a, b∈ Z}이 factorization domain이지만 unique factorization domain가 아닌 것을 증명하였다. 그리고 integral domain인 D=Z[√-p]와 D=Z[√2p]이 factorizat -ion domain이지만 unique factorization domain가 아닌 몇 개의 예를 만들었다.