- class sage.categories.semirings.Semirings(base_category)#
The category of semirings.
A semiring \((S,+,*)\) is similar to a ring, but without the requirement that each element must have an additive inverse. In other words, it is a combination of a commutative additive monoid \((S,+)\) and a multiplicative monoid \((S,*)\), where \(*\) distributes over \(+\).
sage: Semirings() Category of semirings sage: Semirings().super_categories() [Category of associative additive commutative additive associative additive unital distributive magmas and additive magmas, Category of monoids] sage: sorted(Semirings().axioms()) ['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveUnital', 'Associative', 'Distributive', 'Unital'] sage: Semirings() is (CommutativeAdditiveMonoids() & Monoids()).Distributive() True sage: Semirings().AdditiveInverse() Category of rings