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Spring 2007 Big indecomposable modules and direct-sum relations
Wolfgang Hassler, Ryan Karr, Lee Klingler, Roger Wiegand
Illinois J. Math. 51(1): 99-122 (Spring 2007). DOI: 10.1215/ijm/1258735327

Abstract

A commutative Noetherian local ring $(R,\m)$ is said to be \emph{Dedekind-like} provided $R$ has Krull-dimension one, $R$ has no non-zero nilpotent elements, the integral closure $\overline R$ of $R$ is generated by two elements as an $R$-module, and $\m$ is the Jacobson radical of $\overline R$. A classification theorem due to Klingler and Levy implies that if $M$ is a finitely generated indecomposable module over a Dedekind-like ring, then, for each minimal prime ideal $P$ of $R$, the vector space $M_P$ has dimension $0, 1$ or $2$ over the field $R_P$. The main theorem in the present paper states that if $R$ (commutative, Noetherian and local) has non-zero Krull dimension and is not a homomorphic image of a Dedekind-like ring, then there are indecomposable modules that are free of any prescribed rank at each minimal prime ideal.

Citation

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Wolfgang Hassler. Ryan Karr. Lee Klingler. Roger Wiegand. "Big indecomposable modules and direct-sum relations." Illinois J. Math. 51 (1) 99 - 122, Spring 2007. https://doi.org/10.1215/ijm/1258735327

Information

Published: Spring 2007
First available in Project Euclid: 20 November 2009

zbMATH: 1129.13010
MathSciNet: MR2346189
Digital Object Identifier: 10.1215/ijm/1258735327

Subjects:
Primary: 13C13
Secondary: 13D07, 13F05

Rights: Copyright © 2007 University of Illinois at Urbana-Champaign

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Vol.51 • No. 1 • Spring 2007
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