Abbreviation: DpAlg

A \emph{distributive p-algebra} is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1,^*\rangle$ such that

$\langle L,\vee,0,\wedge,1\rangle$ is a bounded distributive lattices

$x^*$ is the \emph{pseudo complement} of $x$: $y\leq x^* \iff x\wedge y=0$

Let $\mathbf{L}$ and $\mathbf{M}$ be distributive p-algebras. A morphism from $\mathbf{L}$ to $\mathbf{M}$ is a function $h:L\rightarrow M$ that is a homomorphism:

$h(x\vee y)=h(x)\vee h(y)$, $h(x\wedge y)=h(x)\wedge h(y)$, $h(0)=0$, $h(1)=1$, $h(x^*)=h(x)^*$

Example 1:

$\begin{array}{lr} f(1)= &1 f(2)= &1 f(3)= &1 f(4)= & f(5)= & f(6)= & f(7)= & \end{array}$

Distributive double p-algebras

Distributive lattices