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Finite Field

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A finite field is a field with a finite number of elements. In such a field, the number of elements is always a power of a prime.

Finite field is a college-level concept that would be first encountered in an abstract algebra course covering rings and fields.

Prerequisites

Congruence: A congruence is an equation in modular arithmetic, i.e., one in which only the remainders relative to some base, known as the "modulus," are significant.
Field: A field is a ring in which every nonzero element has a multiplicative inverse. The real numbers and the complex numbers are both fields.

Classroom Articles on Rings and Fields

  • Algebra
  • Ideal
  • Algebraic Number
  • Quaternion
  • Gaussian Integer
  • Ring

  • Classroom Articles on Abstract Algebra (Up to College Level)

  • Abelian Group
  • Group Representation
  • Abstract Algebra
  • Group Theory
  • Boolean Algebra
  • Isomorphism
  • Cyclic Group
  • Normal Subgroup
  • Dihedral Group
  • Simple Group
  • Finite Group
  • Subgroup
  • Group
  • Symmetric Group
  • Group Action
  • Symmetry Group