Failure of Krull-Schmidt for invertible lattices over a discrete valuation ring
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- by Esther Beneish PDF
- Proc. Amer. Math. Soc. 134 (2006), 1869-1873 Request permission
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.References
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Additional Information
- Esther Beneish
- Affiliation: Department of Mathematics, Central Michigan University, Mount Pleasant, Michigan 48859
- Email: benei1e@cmich.edu
- 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
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1869-1873
- MSC (2000): Primary 20C10, 20C11
- DOI: https://doi.org/10.1090/S0002-9939-05-08194-3
- MathSciNet review: 2215113