Geodesic
Projective and free ordered modules
Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 41-52.

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The paper introduces the concepts of $o$-free and $o$-projective modules over directed ring $R$. Some sufficient conditions are established under which all $o$-projective $R$-modules are $o$-free. In particular, it is proven that all $o$-projective $R$-modules are $o$-free in the cases: linearly ordered rings $R$ without divisors of zero in which each element $0$ is invertible; commutative factorable domain of integrity with any linear order; commutative rings without divisors of zero in which all projective modules are free with any linear order. 
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     author = {A. V. Mikhalev and M. A. Shatalova},
     title = {Projective and free ordered modules},
     journal = {Matemati\v{c}eskie zametki},
     pages = {41--52},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a5/}
}
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A. V. Mikhalev; M. A. Shatalova. Projective and free ordered modules. Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 41-52. http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a5/