Bases: sage.categories.category_with_axiom.CategoryWithAxiom_singleton
The category of semirings.
A semiring 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
and a multiplicative monoid
, where
distributes
over
.
EXAMPLES:
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
TESTS:
sage: TestSuite(Semirings()).run()