Semilattices with zero

Abbreviation: Slat$_0$

Definition

A semilattice with zero is a structure $\mathbf{S}=\langle S,\cdot,0\rangle$ of type $\langle 2,0\rangle $ such that

$\langle S,\cdot\rangle$ is a semilattices

$0$ is a zero for $\cdot$: $x\cdot 0=0$

Morphisms

Let $\mathbf{S}$ and $\mathbf{T}$ be semilattices with zero. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\rightarrow T$ that is a homomorphism:

$h(x\cdot y)=h(x)\cdot h(y)$, $h(0)=0$

Examples

Example 1:

Basic results

Properties

Finite members

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

Subclasses

Superclasses

References