Bases: sage.categories.category_with_axiom.CategoryWithAxiom_singleton
The category of rngs.
An rng is similar to a ring but not necessarilly
unital. In other words, it is a combination of a commutative
additive group
and a multiplicative semigroup
,
where
distributes over
.
EXAMPLES:
sage: C = Rngs(); C
Category of rngs
sage: sorted(C.super_categories(), key=str)
[Category of associative additive commutative additive associative additive unital distributive magmas and additive magmas,
Category of commutative additive groups]
sage: sorted(C.axioms())
['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveInverse',
'AdditiveUnital', 'Associative', 'Distributive']
sage: C is (CommutativeAdditiveGroups() & Semigroups()).Distributive()
True
sage: C.Unital()
Category of rings
TESTS:
sage: TestSuite(C).run()