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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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