PRIME IDEALS IN THE PRODUCT OF COMMUTATIVE RINGS WITH IDENTITY

For the collection {R(alpha)} of commutative rings with identity (alph a is-an-element-of A), let [GRAPHICS]. We define a map C from R to a c ertain 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 ultr afilters) on C and find necessary and sufficient conditions for C to b e a homeomorphism from Minspec(R) to the space of minimal prime filter s on L. Finitely generated prime ideals are characterized and it is sh own that C is a homeomorphism from Spec(R) to the space of prime filte rs on L if and only if R has finite Krull dimension. A special class o f primes is considered in the general case and two more classes of pri mes are considered when each R(alpha) is a Dedekind domain.