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

Sage Live

C = Domains(); C
C.super_categories()
C is Rings().NoZeroDivisors()

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]

Sage Live

Domains().super_categories()