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

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

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

## Abstract

Let A_{K} denote the ring of algebraic integers of an algebraic number field K = Q(θ) where the algebraic integer θ has minimal polynomial F(x) = x^{n} + ax^{m} + 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 [A_{K} : Z[θ]] when u = 0 or u divides m; such primes p are important for explicitly determining the decomposition of pA_{K} into a product of prime ideals of A_{K} 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 A_{K} to be equal to Z[θ].

Item Type: | Article |
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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 |

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