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'>
>>> from sage.all import *
>>> MS = MatrixSpace(QQ, Integer(3), Integer(3)) # needs sage.modules
>>> type(MS.ideal(MS.one()).parent()) # needs sage.modules
<class 'sage.rings.ideal_monoid.IdealMonoid_c_with_category'>
- sage.rings.ideal_monoid.IdealMonoid(R)[source]#
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
>>> from sage.all import * >>> R = QQ['x'] >>> from sage.rings.ideal_monoid import IdealMonoid >>> IdealMonoid(R) Monoid of ideals of Univariate Polynomial Ring in x over Rational Field
- class sage.rings.ideal_monoid.IdealMonoid_c(R)[source]#
Bases:
Parent
The monoid of ideals in a commutative ring.
- Element[source]#
alias of
Ideal_generic
- ring()[source]#
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
>>> from sage.all import * >>> R = QuadraticField(-Integer(23), 'a') # needs sage.rings.number_field >>> from sage.rings.ideal_monoid import IdealMonoid >>> M = IdealMonoid(R); M.ring() is R # needs sage.rings.number_field True