Commutative algebras¶
- class sage.categories.commutative_algebras.CommutativeAlgebras(base_category)[source]¶
- Bases: - CategoryWithAxiom_over_base_ring- The category of commutative algebras with unit over a given base ring. - EXAMPLES: - sage: M = CommutativeAlgebras(GF(19)) sage: M Category of commutative algebras over Finite Field of size 19 sage: CommutativeAlgebras(QQ).super_categories() [Category of algebras over Rational Field, Category of commutative rings] - >>> from sage.all import * >>> M = CommutativeAlgebras(GF(Integer(19))) >>> M Category of commutative algebras over Finite Field of size 19 >>> CommutativeAlgebras(QQ).super_categories() [Category of algebras over Rational Field, Category of commutative rings] - This is just a shortcut for: - sage: Algebras(QQ).Commutative() Category of commutative algebras over Rational Field - >>> from sage.all import * >>> Algebras(QQ).Commutative() Category of commutative algebras over Rational Field - Todo - product ( = Cartesian product) 
- coproduct ( = tensor product over base ring) 
 - class TensorProducts(category, *args)[source]¶
- Bases: - TensorProductsCategory- The category of commutative algebras constructed by tensor product of commutative algebras. - extra_super_categories()[source]¶
- EXAMPLES: - sage: Algebras(QQ).Commutative().TensorProducts().extra_super_categories() [Category of commutative rings] sage: Algebras(QQ).Commutative().TensorProducts().super_categories() [Category of tensor products of algebras over Rational Field, Category of commutative algebras over Rational Field] - >>> from sage.all import * >>> Algebras(QQ).Commutative().TensorProducts().extra_super_categories() [Category of commutative rings] >>> Algebras(QQ).Commutative().TensorProducts().super_categories() [Category of tensor products of algebras over Rational Field, Category of commutative algebras over Rational Field]