Answer to Question #25098 in Abstract Algebra for Rebecca

Question

a) For the quadratic x^2-cx+d, with c, d integers and roots alpha & alpha-hat which are not integers. Establish that if |c|+|d| is less than or equal to 2, then Z[alpha] is a Euclidean Domain.

b) Find all such Z[alpha]'s satisfying the conditions of (a)