Domains#

class sage.categories.domains.Domains(base_category)[source]#

Bases: CategoryWithAxiom_singleton

The category of domains

A domain (or non-commutative integral domain), is a ring, not necessarily commutative, with no nonzero zero divisors.

EXAMPLES:

Sage

sage: C = Domains(); C
Category of domains
sage: C.super_categories()
[Category of rings]
sage: C is Rings().NoZeroDivisors()
True

Python

>>> from sage.all import *
>>> C = Domains(); C
Category of domains
>>> C.super_categories()
[Category of rings]
>>> C is Rings().NoZeroDivisors()
True

Commutative[source]#: alias of IntegralDomains

class ElementMethods[source]#: Bases: object

class ParentMethods[source]#: Bases: object

super_categories()[source]#

EXAMPLES:

Sage

sage: Domains().super_categories()
[Category of rings]

Python

>>> from sage.all import *
>>> Domains().super_categories()
[Category of rings]