Algebra modules

class sage.categories.algebra_modules.AlgebraModules(A)

Bases: sage.categories.category_types.Category_module

The category of modules over a fixed algebra \(A\).

EXAMPLES:

sage: AlgebraModules(QQ['a'])
Category of algebra modules over Univariate Polynomial Ring in a over Rational Field
sage: AlgebraModules(QQ['a']).super_categories()
[Category of modules over Univariate Polynomial Ring in a over Rational Field]

Note: as of now, \(A\) is required to be commutative, ensuring that the categories of left and right modules are isomorphic. Feedback and use cases for potential generalizations to the non commutative case are welcome.

algebra()

EXAMPLES:

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

Returns an instance of this class

EXAMPLES:

sage: AlgebraModules.an_instance()
Category of algebra modules over Univariate Polynomial Ring in x over Rational Field
super_categories()

EXAMPLES:

sage: AlgebraModules(QQ[x]).super_categories()
[Category of modules over Univariate Polynomial Ring in x over Rational Field]

Previous topic

AlgebraIdeals

Next topic

Algebras

This Page