If $G$ is a po-group (ie. partially ordered group), we say that $G$ is po-indecomposable if it's not the direct product of two non trivial subgroups (such subgroups are necessary convex and normal).

If a po-group $G$ has the ACC (ascending chain condition) or the DCC (descending chain condition) on convex normal subgroups, then we may verify that $G$ is a direct product of a finite number of po-indecomposable subgroups.

Can we have the uniqueness of such a decomposition like in the Krull-Schmidt theorem for abstract groups with the ACC or the DCC on normal subgroups.

Are there any articles on the subject ?