Algebra modules¶
- class sage.categories.algebra_modules.AlgebraModules(A)[source]¶
- 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] - >>> 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: AlgebraModules(QQ['x']).algebra() Univariate Polynomial Ring in x over Rational Field - >>> from sage.all import * >>> AlgebraModules(QQ['x']).algebra() Univariate Polynomial Ring in x over Rational Field 
 - classmethod an_instance()[source]¶
- Return an instance of this class. - EXAMPLES: - sage: AlgebraModules.an_instance() Category of algebra modules over Univariate Polynomial Ring in x over Rational Field - >>> 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: AlgebraModules(QQ['x']).super_categories() [Category of modules over Univariate Polynomial Ring in x over Rational Field] - >>> from sage.all import * >>> AlgebraModules(QQ['x']).super_categories() [Category of modules over Univariate Polynomial Ring in x over Rational Field]