Abbreviation: StAlg

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

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

Let $\mathbf{L}$ and $\mathbf{M}$ be Stone 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:

$\begin{array}{lr} f(1)= &1 f(2)= &1 f(3)= &1 f(4)= &2 f(5)= &2 f(6)= &4 f(7)= &5 f(8)= &10 f(9)= &16 f(10)= &28 \end{array}$

Double Stone algebras

Distributive p-algebras