For the collection {Rα} of commutative rings with identity (α ε A), let. We define a map C fromRto a certain cross product and use C to construct a lattice L. We show that C is a homeomorphism from Maxspec(R) to the Stone space (space of ultrafilters) on L and find necessary and sufficient conditions for C to be a homeomorphism from Minspec(R) to the space of minimal prime filters on L. Finitely generated prime ideals are characterized and it is shown that C is a homeomorphism from Spec(R) to the space of prime filters on L if and only ifRhas finite Krull dimension. A special class of primes is considered in the general case and two more classes of primes are considered when each Rαis a Dedekind domain.