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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Unique decomposition into ideals for reduced commutative Noetherian rings


Authors: Başak Ay and Lee Klingler
Journal: Trans. Amer. Math. Soc. 363 (2011), 3703-3716
MSC (2010): Primary 13B21, 13B22, 13B30, 13E05
Published electronically: February 25, 2011
MathSciNet review: 2775824
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Abstract: We say that a commutative ring $ R$ has the unique decomposition into ideals (UDI) property if, for any $ R$-module which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In this paper, we characterize the UDI property for reduced Noetherian rings.


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Additional Information

Başak Ay
Affiliation: Department of Mathematics, Computer Science and Statistics, Ohio State University, Lima, Ohio 45804

Lee Klingler
Affiliation: Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05249-9
PII: S 0002-9947(2011)05249-9
Received by editor(s): March 18, 2009
Received by editor(s) in revised form: October 5, 2009, and November 13, 2009
Published electronically: February 25, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.