In this thesis we study p-algebras and its underlying lattices. An algebra L = ⟨L, ∧, ∨, ∗ , 0, 1⟩ is called a p-algebra if (i) ⟨L, ∧, ∨, 0, 1⟩ is a bounded lattice, and (ii) for all x, y ∈ L, x ∧ x ∗ = 0 and x ∧ y ...