# 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]
```