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Idempotent semirings
Abbreviation: ISRng
Definition
An \emph{idempotent semiring} is a semiring S=⟨S,∨,⋅⟩ such that
∨ is idempotent: x∨x=x
Morphisms
Let S and T be idempotent semirings. A morphism from S to T is a function h:S→T that is a homomorphism:
h(x∨y)=h(x)∨h(y), h(x⋅y)=h(x)⋅h(y)
Examples
Example 1:
Basic results
Properties
Finite members
f(1)=1f(2)=6f(3)=61f(4)=866f(5)=f(6)=