Gcd domains

class sage.categories.gcd_domains.GcdDomains

Bases: Category_singleton

The category of gcd domains domains where gcd can be computed but where there is no guarantee of factorisation into irreducibles

EXAMPLES:

Sage

sage: GcdDomains()
Category of gcd domains
sage: GcdDomains().super_categories()
[Category of integral domains]

Python

>>> from sage.all import *
>>> GcdDomains()
Category of gcd domains
>>> GcdDomains().super_categories()
[Category of integral domains]

class ElementMethods

Bases: object

class ParentMethods

Bases: object

additional_structure()

Return None.

Indeed, the category of gcd domains defines no additional structure: a ring morphism between two gcd domains is a gcd domain morphism.

See also

Category.additional_structure()

EXAMPLES:

Sage

sage: GcdDomains().additional_structure()

Python

>>> from sage.all import *
>>> GcdDomains().additional_structure()

super_categories()

EXAMPLES:

Sage

sage: GcdDomains().super_categories()
[Category of integral domains]

Python

>>> from sage.all import *
>>> GcdDomains().super_categories()
[Category of integral domains]