Monoid of ideals in a commutative ring¶
WARNING: This is used by some rings that are not commutative!
sage: MS = MatrixSpace(QQ,3,3)
sage: type(MS.ideal(MS.one()).parent())
<class 'sage.rings.ideal_monoid.IdealMonoid_c_with_category'>

sage.rings.ideal_monoid.
IdealMonoid
(R)¶ Return the monoid of ideals in the ring
R
.EXAMPLES:
sage: R = QQ['x'] sage: sage.rings.ideal_monoid.IdealMonoid(R) Monoid of ideals of Univariate Polynomial Ring in x over Rational Field

class
sage.rings.ideal_monoid.
IdealMonoid_c
(R)¶ Bases:
sage.structure.parent.Parent
The monoid of ideals in a commutative ring.

Element
¶ alias of
sage.rings.ideal.Ideal_generic

ring
()¶ Return the ring of which this is the ideal monoid.
EXAMPLES:
sage: R = QuadraticField(23, 'a') sage: M = sage.rings.ideal_monoid.IdealMonoid(R); M.ring() is R True
