Monoid of ideals in a commutative ring#
WARNING: This is used by some rings that are not commutative!
sage: MS = MatrixSpace(QQ, 3, 3) # needs sage.modules
sage: type(MS.ideal(MS.one()).parent()) # needs 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') # needs sage.rings.number_field sage: from sage.rings.ideal_monoid import IdealMonoid sage: M = IdealMonoid(R); M.ring() is R # needs sage.rings.number_field True