Decomposition of rational primes in biquadratic fields

Abstract

The ring of integers of a number field may be not a UFD, i.e. a nonzero nonunit element may be written as different products of irreducible elements. But for the ideal levels, we have that every nonzero proper ideal can be represented uniquely as the product of prime ideals. The study of the decomposition of the rational primes in various types of number fields is one of the interesting topics. The de-composition of rational primes in a quadratic field can be determined completely. In this thesis we will determine the decomposition of rational primes in a bi-quadratic field K = Q ([square root]m, [square root]n), where m, n are squarefree integers.