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

$\begin{array}{lr} f(1)= &1
f(2)= &6
f(3)= &61
f(4)= &866
f(5)= &
f(6)= &
\end{array}$

Subclasses

Idempotent semirings with identity

Idempotent semirings with zero

Superclasses

Semirings

References