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Failure of Krull-Schmidt for invertible lattices over a discrete valuation ring

Author(s): Esther Beneish
Journal: Proc. Amer. Math. Soc. 134 (2006), 1869-1873.
MSC (2000): Primary 20C10, 20C11
Posted: December 19, 2005
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Abstract: Let $ p$ be a prime greater than $ 3$, and let $ N$ be the semi-direct product of a group $ H$ of order $ p$ by a cyclic $ C$ group of order $ p-1$, which acts faithfully on $ H$. Let $ R$ be the localization of $ Z$ at $ p$. We show that the Krull-Schmidt Theorem fails for the category of invertible $ RN$-lattices.

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Additional Information:

Esther Beneish
Affiliation: Department of Mathematics, Central Michigan University, Mount Pleasant, Michigan 48859
Email: benei1e@cmich.edu

DOI: 10.1090/S0002-9939-05-08194-3
PII: S 0002-9939(05)08194-3
Keywords: Permutation lattices, invertible lattices, Krull-Schmidt
Received by editor(s): September 8, 2004
Received by editor(s) in revised form: October 24, 2004 and February 5, 2005
Posted: December 19, 2005
Additional Notes: This research was partially supported by NSF grant \#DMS-0244766
Communicated by: Martin Lorenz
Copyright of article: Copyright 2005, American Mathematical Society

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