Algebra modules - Category Framework

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# Algebra modules

class sage.categories.algebra_modules.AlgebraModules(A)

  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()

    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()

    Return 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()

    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]