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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A note on stable equivalence and Nakayama algebras


Author: Idun Reiten
Journal: Proc. Amer. Math. Soc. 71 (1978), 157-163
MSC: Primary 16A46; Secondary 16A35, 16A64
MathSciNet review: 500481
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0500481-7
PII: S 0002-9939(1978)0500481-7
Keywords: Nakayama algebra, stable equivalence
Article copyright: © Copyright 1978 American Mathematical Society