Table of Contents
Distributive p-algebras
Abbreviation: DpAlg
Definition
A 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 pseudo complement of $x$: $y\leq x^* \iff x\wedge y=0$
Morphisms
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 $, $h(1)=1$, $h(x^*)=h(x)^*$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr} f(1)= &1\\ f(2)= &1\\ f(3)= &1\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ f(7)= &\\ \end{array}$
Subclasses
Superclasses
References
Trace: » distributive_p-algebras