# Rngs¶

class sage.categories.rngs.Rngs(base_category)

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

Unital