Monoid of ideals in a commutative ring

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