# Semirngs¶

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 $$+$$.

EXAMPLES:

sage: Semirings()
Category of semirings
sage: Semirings().super_categories()
Category of monoids]

sage: sorted(Semirings().axioms())

sage: Semirings() is (CommutativeAdditiveMonoids() & Monoids()).Distributive()
True

Category of rings


TESTS:

sage: TestSuite(Semirings()).run()


Semigroups

Sets