σ-ideals of Distributive p-algebras

The concepts of boosters and $σ$-ideals are introduced in distributive p-algebras. Many properties of $σ$-ideals are studied in terms of boosters. It is proved that the class of all boosters of a distributive p-algebra is a Boolean algebra. It is also observed that the lattice of all $σ$-ideals of a distributive p-algebra is isomorphic to the ideal lattice of the lattice of all boosters. Finally, some properties of $σ$-ideals are studied with respect to homomorphisms.