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by Ciro Santilli (@cirosantilli, 37)

Classification of finite fields

 ... Area of mathematics Algebra Group Ring (mathematics) Field (mathematics) Finite field
 0 By others on same topic  0 Discussions  Updated 2025-05-26  +Created 1970-01-01  See my version
Tags: Classification
There's exactly one field per prime power, so all we need to specify a field is give its order, notated e.g. as GF(n).
Every element of a finite field satisfies xorder=x.
It is interesting to compare this result philosophically with the classification of finite groups: fields are more constrained as they have to have two operations, and this leads to a much simpler classification!

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  1. Finite field
  2. Field (mathematics)
  3. Ring (mathematics)
  4. Group
  5. Algebra
  6. Area of mathematics
  7. Mathematics
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 Incoming links (6)

  • Classification (mathematics)
  • Classification of finite rings
  • Finite field of non-prime order
  • Finite general linear group
  • Isomorphism
  • Prime power

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