Commutative algebras#

class sage.categories.commutative_algebras.CommutativeAlgebras(base_category)#

Bases: CategoryWithAxiom_over_base_ring

The category of commutative algebras with unit over a given base ring.

EXAMPLES:

sage: M = CommutativeAlgebras(GF(19))                                           # optional - sage.rings.finite_rings
sage: M                                                                         # optional - sage.rings.finite_rings
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]

This is just a shortcut for:

sage: Algebras(QQ).Commutative()
Category of commutative algebras over Rational Field

Todo

  • product ( = Cartesian product)

  • coproduct ( = tensor product over base ring)

class TensorProducts(category, *args)#

Bases: TensorProductsCategory

The category of commutative algebras constructed by tensor product of commutative algebras.

extra_super_categories()#

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]