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