### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »

# Finite Fields

class `sage.categories.finite_fields.``FiniteFields`(base_category)

  Bases: `sage.categories.category_with_axiom.CategoryWithAxiom_singleton`

  The category of finite fields.

  EXAMPLES:

      sage: K = FiniteFields()
      sage: K
      Category of finite fields

  A finite field is a finite monoid with the structure of a field:

      sage: K.super_categories()
      [Category of fields, Category of finite commutative rings]

  Some examples of membership testing and coercion:

      sage: FiniteField(17) in K
      True
      sage: RationalField() in K
      False
      sage: K(RationalField())
      Traceback (most recent call last):
      ...
      TypeError: unable to canonically associate a finite field to Rational Field

  TESTS:

      sage: TestSuite(FiniteFields()).run()
      sage: FiniteFields().is_subcategory(FiniteEnumeratedSets())
      True

  class `ElementMethods`
  class `FiniteFields.``ParentMethods`

### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »