Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Algebra Field & Field Extensions
A quadratic field is called a simple quadratic field if:
1
it also follows that πi is associate of some yj and conversely.
2
divisor, unity, associate and prime in Q(w) are same as those in k(i).
3
the representation is unique apart from the order of the primes, the presence of unities and ambiguities between associated primes.
4
every algebraic integer can be expressed as a product of prime element uniquely up to change of order and multiplication by units.