Bases: sage.categories.category.Category
The category of commutative rings
commutative rings with unity, i.e. rings with commutative * and a multiplicative identity
EXAMPLES:
sage: CommutativeRings()
Category of commutative rings
sage: CommutativeRings().super_categories()
[Category of rings]
TESTS:
sage: TestSuite(CommutativeRings()).run()
sage: QQ['x,y,z'] in CommutativeRings()
True
sage: GroupAlgebra(DihedralGroup(3), QQ) in CommutativeRings()
False
sage: MatrixSpace(QQ,2,2) in CommutativeRings()
False
GroupAlgebra should be fixed:
sage: GroupAlgebra(CyclicPermutationGroup(3), QQ) in CommutativeRings() # todo: not implemented
True
EXAMPLES:
sage: CommutativeRings().super_categories()
[Category of rings]