Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). The main result in this paper says that if there exists a completely regular Hausdorff space X such that E is Riesz algebra isomorphic to C(X) then for every i ∈ I there exists a completely regular Hausdorff space X, such that B(ei) is Riesz algebra isomorphic to C(Xi). Under an additional condition the inverse holds.
