Global Dimensions of Some Artinian Algebras

Atabey Kaygun; M\"uge Kanuni

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arxiv 1206.3726 v2 pith:X5XYIJIA submitted 2012-06-17 math.RA math.KT

Global Dimensions of Some Artinian Algebras

M\"uge Kanuni , Atabey Kaygun This is my paper

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keywords artinianglobaldimensionsalgebraalgebrasalgorithmboundsdimension

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In this article we obtain lower and upper bounds for global dimensions of a class of artinian algebras in terms of global dimensions of a finite subset of their artinian subalgebras. Finding these bounds for the global dimension of an artinian algebra $A$ is realized via an explicit algorithm we develop. This algorithm is based on a directed graph (not the Auslander-Reiten quiver) we construct, and it allows us to decide whether an artinian algebra has finite global dimension in good number of cases.

Global Dimensions of Some Artinian Algebras

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