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]