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