Geodesic
Pure projective modules over exceptional uniserial noncoherent rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 3, pp. 67-84

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We classify pure projective modules over an arbitrary exceptional chain noncoherent ring $R$. In particular, we show that there exists a pure projective $R$-module admitting no indecomposable decomposition, but every pure projective module contains an indecomposable direct summand. 
@article{FPM_2012_17_3_a5,
     author = {G. E. Puninski},
     title = {Pure projective modules over exceptional uniserial noncoherent rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {67--84},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_3_a5/}
}
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G. E. Puninski. Pure projective modules over exceptional uniserial noncoherent rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 3, pp. 67-84. http://geodesic.mathdoc.fr/item/FPM_2012_17_3_a5/