Xiang Yun XIE(1),Yong Lin CAO(
In this paper, some characterizations for an ordered semigroup S to be a semilattice of archimedean semigroups, in particular, a chain of archimedeam subsemi-groups are given by some binary relations on S and the properties of radical subset of the ideals of S. The result that every semiprime ideal of S is the intersection of prime ideals containing it is proved by the concept of m-system of S. Furthermore, using the prime radical theorem, we prove that an ordered semigroup S is a chain of archimedean semigroups if and only if S is a semillatice of archimedean semigroups and all prime ieals of S is a chain. As an application the corresponding results [1] on semigroups without orders can be obtained by moderate modificaitons.