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 \(+\).

See: http://en.wikipedia.org/wiki/Semiring

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]

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