Field theory and polynomials Finite fields Concept
Finite field
Summary
A finite field is a field with a finite number of elements. For each prime power there is exactly one finite field of order , up to isomorphism, and there are no other finite fields. The definition of a finite field states it.
Where this leads
36 pages build on this one.
- Fractional factorial design
- Cap set problem
- Near-field
- Blocking set
- Finite Desarguesian planes are Pappian
- Hasse–Weil zeta function
- Modular representation theory
- Hasse's theorem on elliptic curves
- Elementary abelian group
- Galois ring
- Ovoid
- Deligne–Lusztig theory
- Arc in a finite plane
- Gross–Zagier theorem
- Modularity theorem
- Projective geometry over a finite field
- Ulm's theorem
- Jacobi sum
- Spread
- Multiply transitive group action
- Kakeya problem over finite fields
- Ax–Grothendieck theorem
- Congruent number problem
- Decomposition group
- Pseudo algebraically closed field
- Global field
- Serre's modularity conjecture
- Affine plane over a finite field
- Group of Lie type
- Segre's theorem
- Möbius–Kantor configuration
- Sato–Tate conjecture
- Gauss sum
- Unital
- Frobenius group
- Birch and Swinnerton-Dyer conjecture
Further reading
- Web https://en.wikipedia.org/wiki/Finite_field, lead section
About this page
| Tag | 0ZXZ82FTX2 |
|---|---|
| URI | m2://0ZXZ82FTX2 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 12E20 |
| Specializes | Field |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Definitions
Used by
- Fractional factorial design
- Cap set problem
- Near-field
- Finite Desarguesian planes are Pappian
- Hasse–Weil zeta function
- Modular representation theory
- Hasse's theorem on elliptic curves
- Elementary abelian group
- Galois ring
- Ovoid
- Deligne–Lusztig theory
- Modularity theorem
- Projective geometry over a finite field
- Ulm's theorem
- Jacobi sum
- Spread
- Multiply transitive group action
- Kakeya problem over finite fields
- Ax–Grothendieck theorem
- Decomposition group
- Pseudo algebraically closed field
- Global field
- Serre's modularity conjecture
- Affine plane over a finite field
- Group of Lie type
- Segre's theorem
- Sato–Tate conjecture
- Gauss sum
- Unital
- Frobenius group
- Birch and Swinnerton-Dyer conjecture