# Semirings¶

class sage.categories.semirings.Semirings(s=None)

Bases: sage.categories.category_singleton.Category_singleton

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 commutative additive monoids, Category of monoids]


TESTS:

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

class ParentMethods
Semirings.super_categories()

EXAMPLES:

sage: Semirings().super_categories()
[Category of commutative additive monoids, Category of monoids]


Semigroups

Sets