Indecomposables live in all smaller lengths

Ringel CM (2011)
Bulletin of the London Mathematical Society 43(4): 655-660.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Let Lambda be a finite-dimensional k-algebra with k algebraically closed. Bongartz has recently shown that the existence of an indecomposable. Lambda-module of length n > 1 implies that also indecomposable Lambda-modules of length n - 1 exist. Using a slight modification of his arguments, we strengthen the assertion as follows: If there is an indecomposable module of length n, then there is also an accessible one. Here, the accessible modules are defined inductively, as follows. First, the simple modules are accessible. Second, a module of length n >= 2 is accessible provided it is indecomposable and that there is a submodule or a factor module of length n - 1 which is accessible.
Erscheinungsjahr
2011
Zeitschriftentitel
Bulletin of the London Mathematical Society
Band
43
Ausgabe
4
Seite(n)
655-660
ISSN
0024-6093
Page URI
https://pub.uni-bielefeld.de/record/2326672

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Ringel CM. Indecomposables live in all smaller lengths. Bulletin of the London Mathematical Society. 2011;43(4):655-660.
Ringel, C. M. (2011). Indecomposables live in all smaller lengths. Bulletin of the London Mathematical Society, 43(4), 655-660. doi:10.1112/blms/bdq128
Ringel, C. M. (2011). Indecomposables live in all smaller lengths. Bulletin of the London Mathematical Society 43, 655-660.
Ringel, C.M., 2011. Indecomposables live in all smaller lengths. Bulletin of the London Mathematical Society, 43(4), p 655-660.
C.M. Ringel, “Indecomposables live in all smaller lengths”, Bulletin of the London Mathematical Society, vol. 43, 2011, pp. 655-660.
Ringel, C.M.: Indecomposables live in all smaller lengths. Bulletin of the London Mathematical Society. 43, 655-660 (2011).
Ringel, Claus Michael. “Indecomposables live in all smaller lengths”. Bulletin of the London Mathematical Society 43.4 (2011): 655-660.

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