Geodesic
The Structure of Modules over Hereditary Rings
Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 739-755

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Let $A$ be a bounded hereditary Noetherian prime ring. For an $A$-module $M_A$, we prove that $M$ is a finitely generated projective $A/r(M)$-module if and only if $M$ is a $\pi$-projective finite-dimensional module, and either $M$ is a reduced module or $A$ is a simple Artinian ring. The structure of torsion or mixed $\pi$-projective $A$-modules is completely described. 
@article{MZM_2000_68_5_a9,
     author = {A. A. Tuganbaev},
     title = {The {Structure} of {Modules} over {Hereditary} {Rings}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {739--755},
     publisher = {mathdoc},
     volume = {68},
     number = {5},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2000_68_5_a9/}
}
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A. A. Tuganbaev. The Structure of Modules over Hereditary Rings. Matematičeskie zametki, Tome 68 (2000) no. 5, pp. 739-755. http://geodesic.mathdoc.fr/item/MZM_2000_68_5_a9/