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Indecomposables live in all smaller lengths (2011)

Ringel, C. M.

Oxford University Press

In: Bulletin of the London Mathematical Society

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Publication Date: 2011-11-24

Description: Let be a finite-dimensional k -algebra with k algebraically closed. Bongartz has recently shown that the existence of an indecomposable -module of length n 〉 1 implies that also indecomposable -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.

Print ISSN: 0024-6093

Electronic ISSN: 1469-2120

Topics: Mathematics

Published by Oxford University Press

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