Monoid of ideals in a commutative ring

sage.rings.ideal_monoid.IdealMonoid(R)

Return the monoid of ideals in the ring R.

EXAMPLE:

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.

TESTS:

sage: R = QQ['x']
sage: M = sage.rings.ideal_monoid.IdealMonoid(R)
sage: TestSuite(M).run()
  Failure in _test_category:
...
The following tests failed: _test_elements

(The “_test_category” test fails but I haven’t the foggiest idea why.)

Element

alias of Ideal_generic

ring()

Return the ring of which this is the ideal monoid.

EXAMPLE:

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

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Ideals of commutative rings.

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Generic implementation of one- and two-sided ideals of non-commutative rings.

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