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On the finitistic dimension conjecture of Artin algebras

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
320
Issue
1
Identifiers
DOI: 10.1016/j.jalgebra.2007.12.011
Keywords
  • Artin Algebras
  • Representation Dimension
  • Finitistic Dimension
Disciplines
  • Mathematics

Abstract

Abstract Let A be an Artin algebra and e be an idempotent element of A. We prove that if A has representation dimension at most three, then the finitistic dimension of eAe is finite, and deduce that if quasi-hereditary algebras have representation dimensions at most three, then the finitistic dimension conjecture holds.

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