# AlgebraIdeals¶

class sage.categories.algebra_ideals.AlgebraIdeals(A)

The category of two-sided ideals in a fixed algebra $$A$$.

EXAMPLES:

sage: AlgebraIdeals(FreeAlgebra(QQ,2,'a,b'))
Category of algebra ideals in Free Algebra on 2 generators (a, b) over Rational Field

TODO:
• If useful, implement AlgebraLeftIdeals and AlgebraRightIdeals of which AlgebraIdeals would be a subcategory
• Make AlgebraIdeals(R), return CommutativeAlgebraIdeals(R) when R is commutative
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()
[]