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

Author: Esther Beneish
Journal: Proc. Amer. Math. Soc. 134 (2006), 1869-1873
MSC (2000): Primary 20C10, 20C11
Published electronically: December 19, 2005
MathSciNet review: 2215113
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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

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
Published electronically: December 19, 2005
Additional Notes: This research was partially supported by NSF grant #DMS-0244766
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society