Algebra modules#

class sage.categories.algebra_modules.AlgebraModules(A)[source]#

Bases: Category_module

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

EXAMPLES:

Sage

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]

Python

>>> from sage.all import *
>>> AlgebraModules(QQ['a'])
Category of algebra modules over Univariate Polynomial Ring in a over Rational Field
>>> 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()[source]#

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> AlgebraModules(QQ['x']).algebra()
Univariate Polynomial Ring in x over Rational Field

classmethod an_instance()[source]#

Returns an instance of this class

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> AlgebraModules.an_instance()
Category of algebra modules over Univariate Polynomial Ring in x over Rational Field

super_categories()[source]#

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> AlgebraModules(QQ['x']).super_categories()
[Category of modules over Univariate Polynomial Ring in x over Rational Field]