On prime divisors of the index of an algebraic integer

Jakhar, Anuj ; Khanduja, Sudesh K. ; Sangwan, Neeraj (2016) On prime divisors of the index of an algebraic integer Journal of Number Theory, 166 . pp. 47-61. ISSN 0022-314X

Full text not available from this repository.

Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jnt.2016.02.021


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].

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Rings of Algebraic Integers; Integral Basis and Discriminant
ID Code:112144
Deposited On:23 Jan 2018 12:19
Last Modified:23 Jan 2018 12:19

Repository Staff Only: item control page