Algebra ideals

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()
[]