Commutative algebras

class sage.categories.commutative_algebras.CommutativeAlgebras(base_category)

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)

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