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# 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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