Monoid of ideals in a commutative ring¶
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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
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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.)
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Element
¶ alias of
Ideal_generic
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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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