Various properties of the integers in two quadratic number
fields will be examined. Among these will be the property of unique
prime factorization. When unique prime factorization breaks down,
as will be the case in one of the quadratic number fields, the concept
of ideal numbers will be introduced.
unique...
This thesis studies the question of unique factorization in
quadratic integral domains. In the first chapter many general
theorems and definitions from algebraic number theory are introduced.
The second chapter considers an integral domain in which
unique factorization holds. The necessary theorems to prove
unique factorization are developed. The third...