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# AlgebraIdeals

class `sage.categories.algebra_ideals.``AlgebraIdeals`(A)

  Bases: `sage.categories.category_types.Category_ideal`

  The category of two-sided ideals in a fixed algebra \(A\).

  EXAMPLES:

      sage: AlgebraIdeals(QQ['a'])
      Category of algebra ideals in Univariate Polynomial Ring in a over Rational Field

  Todo

  - Add support for non commutative rings (this is currently not supported by the subcategory `AlgebraModules`).
  - Make `AlgebraIdeals(R)`, return `CommutativeAlgebraIdeals(R)` when `R` is commutative.
  - If useful, implement `AlgebraLeftIdeals` and `AlgebraRightIdeals` of which `AlgebraIdeals` would be a subcategory.
  `algebra`()

    EXAMPLES:

        sage: AlgebraIdeals(QQ[x]).algebra()
        Univariate Polynomial Ring in x over Rational Field

  `super_categories`()

    The category of algebra modules should be a super category of this category.

    However, since algebra modules are currently only available over commutative rings, we have to omit it if our ring is non-commutative.

    EXAMPLES:

        sage: AlgebraIdeals(QQ[x]).super_categories()
        [Category of algebra modules over Univariate Polynomial Ring in x over Rational Field]
        sage: C = AlgebraIdeals(FreeAlgebra(QQ,2,'a,b'))
        sage: C.super_categories()
        []

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