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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 more

    Let 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, …

    1893
    Classification theorem of finite fields is first proved by E. H. Moore
    1985
    Basic algebra I is published by Nathan Jacobson
    1994
    Galois field is defined in the Encyclopedia of Mathematics
    2001
    Finite Fields is defined in the Encyclopedia of Mathematics
    2007
    Finite Fields and Applications I is published by Gary L. Mullen and Carl Mummert
    2013
    Handbook of Finite Fields is published by Gary L. Mullen and Daniel Panario

    Non-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 more

    In 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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  2. Finite Fields | Brilliant Math & Science Wiki

  3. Finite Field -- from Wolfram MathWorld

  4. 22.1: Structure of a Finite Field - Mathematics LibreTexts

  5. 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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