Algebra ideals¶
- class sage.categories.algebra_ideals.AlgebraIdeals(A)[source]¶
- Bases: - 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 - >>> from sage.all import * >>> 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- Ris commutative.
- If useful, implement - AlgebraLeftIdealsand- AlgebraRightIdealsof which- AlgebraIdealswould be a subcategory.
 - algebra()[source]¶
- EXAMPLES: - sage: AlgebraIdeals(QQ['x']).algebra() Univariate Polynomial Ring in x over Rational Field - >>> from sage.all import * >>> AlgebraIdeals(QQ['x']).algebra() Univariate Polynomial Ring in x over Rational Field 
 - super_categories()[source]¶
- 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')) # needs sage.combinat sage.modules sage: C.super_categories() # needs sage.combinat sage.modules [] - >>> from sage.all import * >>> AlgebraIdeals(QQ['x']).super_categories() [Category of algebra modules over Univariate Polynomial Ring in x over Rational Field] >>> C = AlgebraIdeals(FreeAlgebra(QQ, Integer(2), 'a,b')) # needs sage.combinat sage.modules >>> C.super_categories() # needs sage.combinat sage.modules []