• Corpus ID: 119663110

Normal elements in finite fields

  title={Normal elements in finite fields},
  author={Trevor Hyde},
  journal={arXiv: Number Theory},
  • Trevor Hyde
  • Published 6 September 2018
  • Mathematics
  • arXiv: Number Theory
We give a simple derivation of the formula for the number of normal elements in an extension of finite fields. Our proof is based on the fact that units in the Galois group ring of a field extension act simply transitively on normal elements. 
Existence and Cardinality of k-Normal Elements in Finite Fields
This paper forms a general lower bound for the number of k-normal elements, assuming that they exist, and derives a new existence condition for k- normal elements using the general factorization of the polynomial $x^m - 1$ into cyclotomic polynomials.


Algebraic Groups and Class Fields
Summary of the main results algebraic curves maps from a curve to a commutative group singular algebraic curves generalized jacobians class field theory group extension and cohomology.
Around Kummer theories
We establish several theories of Kummer type in connection with the unit group scheme of a group algebra, following a method presented by Serre in ⟨Groupes alg ebriques et corps de classes⟩. The
Normal generators of finite fields
Contributions to the theory of finite fields
The present paper contains a number of results in the theory of finite fields or higher congruences. The method may be considered as an appUcation of the theory of /»-polynomials, which I have
Normal Bases over Finite Fields
The principal result in the thesis is the complete determination of all optimal normal bases in finite fields, which confirms a conjecture by Mullin, Onyszchuk, Vanstone and Wilson.
Primitive normal bases for finite fields
It is proved that any finite extension of a finite field has a normal basis consisting of primitive roots. Introduction. Let q be a prime power, q > 1. We denote by F9 a finite field of q elements.
Number Theory in Function Fields
Polynomials over Finite Fields.- Primes, Arithmetic Functions, and the Zeta Function.- The Reciprocity Law.- Dirichlet L-series and Primes in an Arithmetic Progression.- Algebraic Function Fields and
THIS is a text–book intended primarily for undergraduates. It is designed to give a broad basis of knowledge comprising such theories and theorems in those parts of algebra which are mentioned in the
Ueber die Darstellung der Zahlen eines Gattungsbereiches für einen beliebigen Primdivisor.
In einer früheren Arbeit (dieses Journal Bd. 101) habe ich die ganzen algebraischen Zahlen eines beliebigen Gattungsbereiches (G) für irgend einen Primdivisor (P) einer reellen Primzahl p untersucht