Algebra modules

class sage.categories.algebra_modules.AlgebraModules(A)

Bases: 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]