کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593262 1630648 2016 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On prime divisors of the index of an algebraic integer
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On prime divisors of the index of an algebraic integer
چکیده انگلیسی

Let AKAK denote the ring of algebraic integers of an algebraic number field K=Q(θ)K=Q(θ) where the algebraic integer θ   has minimal polynomial F(x)=xn+axm+bF(x)=xn+axm+b over the field QQ of rational numbers with n=mt+un=mt+u, t∈Nt∈N, 0≤u≤m−10≤u≤m−1. In this paper, we characterize those primes which divide the discriminant of F(x)F(x) but do not divide [AK:Z[θ]][AK:Z[θ]] when u=0u=0 or u divides m; such primes p   are important for explicitly determining the decomposition of pAKpAK into a product of prime ideals of AKAK 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 AKAK to be equal to Z[θ]Z[θ].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 166, September 2016, Pages 47–61
نویسندگان
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