Normal integral bases for infinite abelian extensions
نویسندگان
چکیده
منابع مشابه
Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields
Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x), h(x)) = δg,h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char(E) 6= 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char(E) = 2, then F ...
متن کاملNormal integral bases for A4 extensions of the rationals
We give an algorithm for constructing normal integral bases of tame Galois extensions of the rationals with group A4. Using earlier works we can do the same until degree 15.
متن کاملOn integral bases in relative quadratic extensions
Let F be an algebraic number field and E a quadratic extension with E = F(√μ). We describe a minimal set of elements for generating the integral elements oE of E as an oF module. A consequence of this theoretical result is an algorithm for constructing such a set. The construction yields a simple procedure for computing an integral basis of E as well. In the last section, we present examples of...
متن کاملAbelian Groups, Gauss Periods, and Normal Bases
A result on finite abelian groups is first proved and then used to solve problems in finite fields. Particularly, all finite fields that have normal bases generated by general Gauss periods are characterized and it is shown how to find normal bases of low complexity. Dedicated to Professor Chao Ko on his 90th birthday.
متن کاملCounting Generators of Normal Integral Bases
We present a very accurate formula counting norms of normal integral bases in tame abelian extensions of the rational eld. The methods used include applications of Schmidt's Subspace Theorem, Baker's Theorem and the Hardy-Littlewood Method, all from diophantine approximation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2001
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa100-1-7