Countable indecomposable dispersed order types

In this paper we consider some properties of indecomposable dispersed order types and estimate the cardinality of the set of distinct indecomposable order types of given rank which can be represented in the form of the product of order types which are not unity. In addition, we refute Rotman's proposition that every countable indecomposable dispersed order type is, to within equivalence, the finite product of order types of the form $\omega^k$, $(\omega^k)^*$, $\gamma_i$, $\gamma_i^*$, where $k$ is arbitrary, and $i$ is the limiting ordinal.