PrincipalIdealDomains

class sage.categories.principal_ideal_domains.PrincipalIdealDomains(s=None)

Bases: sage.categories.category.Category

The category of (constructive) principal ideal domains

By constructive, we mean that a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.

EXAMPLES:

sage: PrincipalIdealDomains()
Category of principal ideal domains
sage: PrincipalIdealDomains().super_categories()
[Category of gcd domains]

See also: http://en.wikipedia.org/wiki/Principal_ideal_domain

TESTS:

sage: TestSuite(PrincipalIdealDomains()).run()

class ElementMethods

class PrincipalIdealDomains.ParentMethods

PrincipalIdealDomains.super_categories(*args, **kwds)

EXAMPLES:

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