Bases: sage.categories.category_with_axiom.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]
This is just a shortcut for:
sage: Algebras(QQ).Commutative()
Category of commutative algebras over Rational Field
TESTS:
sage: Algebras(QQ).Commutative() is CommutativeAlgebras(QQ)
True
sage: TestSuite(CommutativeAlgebras(ZZ)).run()
Todo:
- product ( = cartesian product)
- coproduct ( = tensor product over base ring)