Table of Contents
Idempotent semirings
Abbreviation: ISRng
Definition
An \emph{idempotent semiring} is a semiring $\mathbf{S}=\langle S,\vee ,\cdot \rangle $ such that
$\vee $ is idempotent: $x\vee x=x$
Morphisms
Let $\mathbf{S}$ and $\mathbf{T}$ be idempotent semirings. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\to T$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr}
f(1)= &1
f(2)= &6
f(3)= &61
f(4)= &866
f(5)= &
f(6)= &
\end{array}$
