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 - RingLeftIdealsand- RingRightIdealsof which- RingIdealswould be a subcategory.
- Make - RingIdeals(R), return- CommutativeRingIdeals(R)when- Ris 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]