Unique decomposition into ideals for reduced commutative Noetherian rings
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- by Başak Ay and Lee Klingler PDF
- Trans. Amer. Math. Soc. 363 (2011), 3703-3716 Request permission
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.References
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Additional Information
- Başak Ay
- Affiliation: Department of Mathematics, Computer Science and Statistics, Ohio State University, Lima, Ohio 45804
- MR Author ID: 929022
- ORCID: 0000-0003-3448-2776
- Lee Klingler
- Affiliation: Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida 33431
- MR Author ID: 228650
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 3703-3716
- MSC (2010): Primary 13B21, 13B22, 13B30, 13E05
- DOI: https://doi.org/10.1090/S0002-9947-2011-05249-9
- MathSciNet review: 2775824