Geodesic
Representations of third-order matrix rings
Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 235-244.

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Necessary and sufficient conditions are obtained for a ring lying in a third-order matrix algebra over the field of $p$-adic numbers to have a finite number of nonisomorphic indecomposable representations. 
@article{MZM_1970_8_2_a11,
     author = {V. V. Kirichenko},
     title = {Representations of third-order matrix rings},
     journal = {Matemati\v{c}eskie zametki},
     pages = {235--244},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a11/}
}
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V. V. Kirichenko. Representations of third-order matrix rings. Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 235-244. http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a11/