Geodesic
Free ordered modules
Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 477-487.

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We establish the necessary and sufficient condition on a partially ordered set $\mathrm{S}$ such that a free ordered $\mathrm{R}$-module ($\mathrm{R}$ is a linearly ordered ring without divisors of zero) over the set $\mathrm{S}$ is $\mathrm{o}$-isomorphic with a free ordered $\mathrm{R}$-module over a trivially ordered set. 
@article{MZM_1972_12_4_a14,
     author = {A. V. Mikhalev and M. A. Shatalova},
     title = {Free ordered modules},
     journal = {Matemati\v{c}eskie zametki},
     pages = {477--487},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a14/}
}
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A. V. Mikhalev; M. A. Shatalova. Free ordered modules. Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 477-487. http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a14/