Ring ideals

class sage.categories.ring_ideals.RingIdeals(R)

Bases: sage.categories.category_types.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

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()

EXAMPLES:

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

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