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Finite field - Wikipedia
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common … See more
A finite field is a finite set that is a field; this means that multiplication, addition, subtraction and division (excluding division by zero) are defined and satisfy the rules of arithmetic known as the field axioms.
The number of … See moreLet q = p be a prime power, and F be the splitting field of the polynomial
The uniqueness up to isomorphism of splitting fields implies thus that all fields …The set of non-zero elements in GF(q) is an abelian group under the multiplication, of order q – 1. By Lagrange's theorem, there exists a divisor k of … See more
If F is a finite field, a non-constant monic polynomial with coefficients in F is irreducible over F, if it is not the product of two non-constant monic polynomials, …
1893Classification theorem of finite fields is first proved by E. H. Moore1985Basic algebra I is published by Nathan Jacobson1994Galois field is defined in the Encyclopedia of Mathematics2001Finite Fields is defined in the Encyclopedia of Mathematics2007Finite Fields and Applications I is published by Gary L. Mullen and Carl Mummert2013Handbook of Finite Fields is published by Gary L. Mullen and Daniel PanarioNon-prime fields
Given a prime power q = p with p prime and n > 1, the field GF(q) may be explicitly constructed in the following way. One …In this section, p is a prime number, and q = p is a power of p.
In GF(q), the identity (x + y) = x + y implies that the map
Denoting by φ the See moreIn cryptography, the difficulty of the discrete logarithm problem in finite fields or in elliptic curves is the basis of several widely used protocols, such as the See more
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Finite Field -- from Wolfram MathWorld
22.1: Structure of a Finite Field - Mathematics LibreTexts
Finite Fields - Cambridge University Press & Assessment
webThe theory of finite fields is a branch of algebra that has come to the fore because of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching ciruits. This book is …
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