Riesz product spaces and representation theory

Let {E-i:i is an element of I} be a family of Archimedean Riesz spaces. The Riesz product space is denoted by Pi(i is an element of I) E-i. The main result in this paper is the following conclusion: There exists a completely regular Hausdorff space X such that Pi(i is an element of I) E-i is Riesz isomorphic to C(X) if and only if for every i is an element of I there exists a completely regular Hausdorff space X-i such that E-i is Riesz isomorphic to C(X-i).