Domains

class sage.categories.domains.Domains(base_category)

Bases: sage.categories.category_with_axiom.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

TESTS:

sage: TestSuite(C).run()
Commutative

alias of IntegralDomains

class ElementMethods
class Domains.ParentMethods
Domains.super_categories()

EXAMPLES:

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

Previous topic

Division rings

Next topic

Enumerated Sets

This Page