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Proceedings of the American Mathematical Society

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



A footnote to the multiplicative basis theorem

Author: William Gustafson
Journal: Proc. Amer. Math. Soc. 95 (1985), 7-8
MSC: Primary 16A46
MathSciNet review: 796436
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Abstract: We characterize those perfect fields $ k$ such that for each integer $ n \geqslant 1$, but there are but finitely many isomorphism types of $ k$-algebras of dimension $ n$ that are of finite representation type. Some remarks on the imperfect case are also presented.

References [Enhancements On Off] (What's this?)

  • [1] R. Bautista, P. Gabriel, A. Roiter and L. Salmerón, Representation-finite algebras and multiplicative bases, preprint, Univ. Nacional Autómoma de México, 1984.
  • [2] Christian U. Jensen and Helmut Lenzing, Homological dimension and representation type of algebras under base field extension, Manuscripta Math. 39 (1982), no. 1, 1–13. MR 672397,
  • [3] Jean-Pierre Serre, Cohomologie galoisienne, With a contribution by Jean-Louis Verdier. Lecture Notes in Mathematics, No. 5. Troisième édition, vol. 1965, Springer-Verlag, Berlin-New York, 1965 (French). MR 0201444
  • [4] E. Steinitz, Algebraische Theorie der Körper, J. Reine Angew. Math. 137 (1910), 167-308.

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Article copyright: © Copyright 1985 American Mathematical Society