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)
, returnCommutativeAlgebraIdeals(R)
whenR
is commutative.If useful, implement
AlgebraLeftIdeals
andAlgebraRightIdeals
of whichAlgebraIdeals
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() []