Table of Contents
Idempotent semirings with identity and zero
Abbreviation: ISRng$_{01}$
Definition
An \emph{idempotent semiring with identity and zero} is a semirings with identity and zero $\mathbf{S}=\langle S,\vee,0,\cdot,1 \rangle $ such that $\vee$ is idempotent: $x\vee x=x$
Morphisms
Let $\mathbf{S}$ and $\mathbf{T}$ be idempotent semirings with identity and zero. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\rightarrow T$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(0)=0$, $h(1)=1$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr}
f(1)= & 1
f(2)= & 1
f(3)= & 3
f(4)= & 20
f(5)= & 149
f(6)= &1488
f(7)= &18554
\end{array}$
