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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Constructive aspects of Noetherian rings
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by Fred Richman
Proc. Amer. Math. Soc. 44 (1974), 436-441
DOI: https://doi.org/10.1090/S0002-9939-1974-0416874-9
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Abstract:

If $R$ is a discrete Noetherian ring, in the sense of Tennenbaum, such that finitely generated ideals are finitely related and detachable, then so is $R[x]$. This shows that a large class of rings enjoy the property that finitely generated ideals are detachable, and that intersections and quotients of finitely generated ideals are finitely generated.
References
    J. B. Tennenbaum, A constructive version of Hilbert’s basis theorem, Ph.D. Dissertation, University of California, San Diego, Calif., 1973.
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 44 (1974), 436-441
  • MSC: Primary 02E99; Secondary 13E05
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0416874-9
  • MathSciNet review: 0416874