We may assume WLOG that . Thus, .
The other bit follows from this.
Try the others and get back to us.
i need to show which of the following are euclidean domains:
a) C[x] with d(f)=deg(f) (where C[x] = set of polynomials with complex coefficients)
b) set of integers with d(n)=|n|+1
c) ring of integers modulo 5 with d(f)=2deg(f)
d) ring of integers modulo 6 with d(f)=deg(f)
e) Z(w) where w=(1+root(-3))/2, with d(z)=|z|^2
i know that an integral domain is a Euclidean domain if it has a Euclidean function but i dont know how to start off the question.
thanks for ur help. heres what i did for the other parts:
c) d(ab)=2deg(ab), b>= and so
d) the ring of integers modulo 6 is not a field.
e) d(w)=|w|^2 = 1/4+3/4=1
(what do i do next?)