Some of the properties of the numbers of two quadratic number
fields are explored. Among these properties is the existence of
unique prime factorization of the integers of the field and the importance
of the concept of ideal numbers in restoring unique factorization
when it does not exist. Some consideration...
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...
This paper is the record of an exploration of two quadratic
number fields. The first section is devoted to the field with elements
of the form a +b√3 where a and b are rational numbers.
This field contains an integral domain in which unique factorization
holds. The second section is...
