Ring ideals#

class sage.categories.ring_ideals.RingIdeals(R)[source]#

Bases: Category_ideal

The category of two-sided ideals in a fixed ring.

EXAMPLES:

sage: Ideals(Integers(200))
Category of ring ideals in Ring of integers modulo 200
sage: C = Ideals(IntegerRing()); C
Category of ring ideals in Integer Ring
sage: I = C([8,12,18])
sage: I
Principal ideal (2) of Integer Ring

>>> from sage.all import *
>>> Ideals(Integers(Integer(200)))
Category of ring ideals in Ring of integers modulo 200
>>> C = Ideals(IntegerRing()); C
Category of ring ideals in Integer Ring
>>> I = C([Integer(8),Integer(12),Integer(18)])
>>> I
Principal ideal (2) of Integer Ring

See also: CommutativeRingIdeals.

Todo

  • If useful, implement RingLeftIdeals and RingRightIdeals of which RingIdeals would be a subcategory.

  • Make RingIdeals(R), return CommutativeRingIdeals(R) when R is commutative.

super_categories()[source]#

EXAMPLES:

sage: RingIdeals(ZZ).super_categories()
[Category of modules over Integer Ring]
sage: RingIdeals(QQ).super_categories()
[Category of vector spaces over Rational Field]

>>> from sage.all import *
>>> RingIdeals(ZZ).super_categories()
[Category of modules over Integer Ring]
>>> RingIdeals(QQ).super_categories()
[Category of vector spaces over Rational Field]