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Large indecomposables over representation-infinite orders and algebras

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Abstract.

Let R be a complete discrete valuation domain with quotient field K, and let Λ be an R-order in a semisimple K-algebra. Butler, Campbell, and Kovács have shown that R-free Λ-modules decompose into Λ-lattices when Λ is representation-finite. Using the theory of ladder functors, we prove the converse by constructing indecomposable R-free Λ-modules of infinite rank if Λ is not representation-finite.

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Authors and Affiliations

  1. Institut für Algebra und Zahlentheorie, Universität Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

    Wolfgang Rump

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  1. Wolfgang Rump
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Correspondence to Wolfgang Rump.

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Received: 23 March 2004

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Rump, W. Large indecomposables over representation-infinite orders and algebras. Arch. Math. 84, 11–21 (2005). https://doi.org/10.1007/s00013-004-1081-4

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  • DOI: https://doi.org/10.1007/s00013-004-1081-4

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