Geodesic
Global dimension of Noetherian serial rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 3, pp. 41-62

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The global dimension of Noetherian serial rings is studied. It is proved that if an indecomposable serial ring has infinite global dimension then it is Artinian and its quiver is a simple cycle. Using methods of the theory of right serial quivers, we give an upper estimate on the Loewy length of Artinian rings of finite global dimension. Applications to the calculation of the global dimension of tiled orders of width 2 are given. 
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     author = {N. A. Bronickaya and V. V. Kirichenko},
     title = {Global dimension of {Noetherian} serial rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {41--62},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_3_a1/}
}
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N. A. Bronickaya; V. V. Kirichenko. Global dimension of Noetherian serial rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 3, pp. 41-62. http://geodesic.mathdoc.fr/item/FPM_2010_16_3_a1/