Geodesic
Projective modules over bounded Dedekind rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 3, pp. 903-911.

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If $A$ is a bounded Dedekind prime ring and $M$ is an $A$-module, then $M$ is a projective module if and only if $M$ is a $\pi$-projective nontorsion module, and either the module $M$ is reduced, or $A$ is a simple Artinian ring. 
@article{FPM_2000_6_3_a19,
     author = {A. A. Tuganbaev},
     title = {Projective modules over bounded {Dedekind} rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {903--911},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a19/}
}
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A. A. Tuganbaev. Projective modules over bounded Dedekind rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 3, pp. 903-911. http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a19/