Commutative rings

class sage.categories.commutative_rings.CommutativeRings(s=None)

Bases: sage.categories.category_singleton.Category_singleton

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
class ElementMethods
class CommutativeRings.ParentMethods
is_commutative()

Return True, since commutative rings are commutative.

EXAMPLES:

sage: Parent(QQ,category=CommutativeRings()).is_commutative()
True
CommutativeRings.super_categories()

EXAMPLES:

sage: CommutativeRings().super_categories()
[Category of rings]

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