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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on stable equivalence and Nakayama algebras
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by Idun Reiten PDF
Proc. Amer. Math. Soc. 71 (1978), 157-163 Request permission

Abstract:

Two artin algebras $\Lambda$ and $\Lambda ’$ are said to be stably equivalent if the categories of finitely generated modules modulo projective for $\Lambda$ and $\Lambda ’$ are equivalent categories. If $\Lambda ’$ is stably equivalent to a Nakayama (i.e. generalized uniserial) algebra $\Lambda$, we prove that $\Lambda$ and $\Lambda ’$ have the same number of nonprojective simple modules. And if $\Lambda$ and $\Lambda ’$ are stably equivalent indecomposable Nakayama algebras where each indecomposable projective module has length at least 3, then $\Lambda$ and $\Lambda ’$ have the same admissible sequences.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 157-163
  • MSC: Primary 16A46; Secondary 16A35, 16A64
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0500481-7
  • MathSciNet review: 500481