The first Brauer-Thrall conjecture

Ringel CM (2008)
In: Models, Modules and Abelian Groups. In Memory of A. L. S. Corner. Göbel R, Goldsmith B (Eds); Berlin: Walter de Gruyter: 369-374.

Sammelwerksbeitrag | Veröffentlicht | Englisch
 
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Herausgeber*in
Göbel, Rüdiger; Goldsmith, Brendan
Abstract / Bemerkung
Let Λ be an artin algebra and M a Λ-module. We show: If M is not the direct sum of copies of a finite number of indecomposable modules of finite length, then M has indecomposable submodules as well as indecomposable factor modules of arbitrarily large finite length. This improves the assertion of the first Brauer–Thrall conjecture as established by Roiter in 1968: Any artin algebra with infinitely many isomorphism classes of indecomposable modules of finite length has indecomposable modules of arbitrarily large finite length.
Stichworte
Artin algebra; modules of finite length; indecomposability; Krull–Remak–Schmidt–Azumaya theorem; Gabriel–Roiter measure; Gabriel–Roiter comeasure; Brauer–Thrall conjectures
Erscheinungsjahr
2008
Buchtitel
Models, Modules and Abelian Groups. In Memory of A. L. S. Corner
Seite(n)
369-374
ISBN
978-3-11-019437-1
Page URI
https://pub.uni-bielefeld.de/record/2940869

Zitieren

Ringel CM. The first Brauer-Thrall conjecture. In: Göbel R, Goldsmith B, eds. Models, Modules and Abelian Groups. In Memory of A. L. S. Corner. Berlin: Walter de Gruyter; 2008: 369-374.
Ringel, C. M. (2008). The first Brauer-Thrall conjecture. In R. Göbel & B. Goldsmith (Eds.), Models, Modules and Abelian Groups. In Memory of A. L. S. Corner (pp. 369-374). Berlin: Walter de Gruyter.
Ringel, C. M. (2008). “The first Brauer-Thrall conjecture” in Models, Modules and Abelian Groups. In Memory of A. L. S. Corner, Göbel, R., and Goldsmith, B. eds. (Berlin: Walter de Gruyter), 369-374.
Ringel, C.M., 2008. The first Brauer-Thrall conjecture. In R. Göbel & B. Goldsmith, eds. Models, Modules and Abelian Groups. In Memory of A. L. S. Corner. Berlin: Walter de Gruyter, pp. 369-374.
C.M. Ringel, “The first Brauer-Thrall conjecture”, Models, Modules and Abelian Groups. In Memory of A. L. S. Corner, R. Göbel and B. Goldsmith, eds., Berlin: Walter de Gruyter, 2008, pp.369-374.
Ringel, C.M.: The first Brauer-Thrall conjecture. In: Göbel, R. and Goldsmith, B. (eds.) Models, Modules and Abelian Groups. In Memory of A. L. S. Corner. p. 369-374. Walter de Gruyter, Berlin (2008).
Ringel, Claus Michael. “The first Brauer-Thrall conjecture”. Models, Modules and Abelian Groups. In Memory of A. L. S. Corner. Ed. Rüdiger Göbel and Brendan Goldsmith. Berlin: Walter de Gruyter, 2008. 369-374.

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