Rngs#
- class sage.categories.rngs.Rngs(base_category)#
Bases:
CategoryWithAxiom_singleton
The category of rngs.
An rng \((S, +, *)\) is similar to a ring but not necessarily unital. In other words, it is a combination of a commutative additive group \((S, +)\) and a multiplicative semigroup \((S, *)\), 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