FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 3, PAGES 41-62

Global dimension of Noetherian serial rings

N. A. Bronickaya
V. V. Kirichenko

Abstract

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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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