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