Finite prime field

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Definition

A finite prime field is a finite field satisfying the folloqing equivalent conditions:

  1. It contains no proper subfield.
  2. Its size is a prime number.

For any prime number p, there is a unique finite prime field of size p, and this is denoted \mathbb{F}_p or GF(p). This is the prime subfield (i.e., the unique smallest subfield) in any field of characteristic p.