Monoid of ideals in a commutative ring

WARNING: This is used by some rings that are not commutative!

sage: MS = MatrixSpace(QQ, 3, 3)                                                    # optional - sage.modules
sage: type(MS.ideal(MS.one()).parent())                                             # optional - sage.modules
<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: from sage.rings.ideal_monoid import IdealMonoid
sage: IdealMonoid(R)
Monoid of ideals of Univariate Polynomial Ring in x over Rational Field

class sage.rings.ideal_monoid.IdealMonoid_c(R)

Bases: Parent

The monoid of ideals in a commutative ring.

Element

alias of Ideal_generic

ring()

Return the ring of which this is the ideal monoid.

EXAMPLES:

sage: R = QuadraticField(-23, 'a')                                          # optional - sage.rings.number_field
sage: from sage.rings.ideal_monoid import IdealMonoid
sage: M = IdealMonoid(R); M.ring() is R                                     # optional - sage.rings.number_field
True