### Table of Contents

## Neardistributive lattices

Abbreviation: **NdLat**

### Definition

A \emph{neardistributive lattice} is a Lattices $\mathbf{L}=\langle L,\vee ,\wedge \rangle $ such that

SD$_{\wedge}^2$: $x\wedge(y\vee z)=x\wedge[y\vee (x\wedge [z\vee(x\wedge y)])]$

SD$_{\vee}^2$: $x\vee(y\wedge z)=x\vee[y\wedge (x\vee [z\wedge(x\vee y)])]$

##### Morphisms

Let $\mathbf{L}$ and $\mathbf{M}$ be neardistributive lattices. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a homomorphism:

$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$

### Examples

Example 1: $D[d]=\langle D\cup\{d'\},\vee ,\wedge\rangle$, where $D$ is any distributive lattice and $d$ is an element in it that is split into two elements $d,d'$ using Alan Day's doubling construction.

### Basic results

### Properties

### Finite members

$\begin{array}{lr}
f(1)= &1

f(2)= &1

f(3)= &1

f(4)= &

f(5)= &

f(6)= &

f(7)= &

\end{array}$