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]