Abstract
Let AK denote the ring of algebraic integers of an algebraic number field K=Q(θ) where the algebraic integer θ has minimal polynomial F(x)=xn+axm+b over the field Q of rational numbers with n=mt+u, t∈N, 0≤u≤m−1. In this paper, we characterize those primes which divide the discriminant of F(x) but do not divide [AK:Z[θ]] when u=0 or u divides m; such primes p are important for explicitly determining the decomposition of pAK into a product of prime ideals of AK in view of the well known Dedekind theorem. As a consequence, we obtain some necessary and sufficient conditions involving only a, b, m, n for AK to be equal to Z[θ].
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