Global Dimensions of Some Artinian Algebras

2012/06/17 by Müge Kanuni̇, Kanuni, Müge, Atabey Kaygun +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1206.3726

openalex publication_date 2012/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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