Free $f$-modules
Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 873-885.

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Let $R$ be a directed ring whose cone of positive elements is strict and satisfies Ore's condition. The main result: there exists a freef-module over an $o$-module $_RM$ with cone $P_M$ if and only if $P_M$ is half-closed (this generalizes Vainberg's theorem for ordered Abelian groups). In this connection various characterizations off-modules with strict cones are given.
@article{MZM_1975_17_6_a4,
     author = {A. V. Mikhalev and M. A. Shatalova},
     title = {Free $f$-modules},
     journal = {Matemati\v{c}eskie zametki},
     pages = {873--885},
     publisher = {mathdoc},
     volume = {17},
     number = {6},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a4/}
}
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A. V. Mikhalev; M. A. Shatalova. Free $f$-modules. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 873-885. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a4/