Fields

class sage.categories.fields.Fields(s=None)

Bases: sage.categories.category.Category

The category of fields commutative fields, i.e. commutative rings where all non-zero elements have multiplicative inverses

EXAMPLES:

sage: K = Fields()
sage: K
Category of fields
sage: Fields().super_categories()
[Category of euclidean domains, Category of unique factorization domains, Category of division rings]

sage: K(IntegerRing())
Rational Field
sage: K(PolynomialRing(GF(3), 'x'))
Fraction Field of Univariate Polynomial Ring in x over
Finite Field of size 3
sage: K(RealField())
Real Field with 53 bits of precision

TESTS:

sage: TestSuite(Fields()).run()

class ElementMethods

class Fields.ParentMethods

Fields.super_categories(*args, **kwds)

EXAMPLES:

sage: Fields().super_categories()
[Category of euclidean domains, Category of unique factorization domains, Category of division rings]