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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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Examples of noncatenary rings
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by Raymond C. Heitmann PDF
Trans. Amer. Math. Soc. 247 (1979), 125-136 Request permission

Abstract:

A technique is developed for constructing a new family of noetherian integral domains. To each domain, there naturally corresponds its poset (partially ordered set) of prime ideals. The resulting family of posets has the following property: every finite poset is isomorphic to a saturated subset of some poset in the family. In the process, it is determined when certain power series may be adjoined to noetherian rings without destroying the noetherian property.
References
  • Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
  • Paul M. Eakin Jr., The converse to a well known theorem on Noetherian rings, Math. Ann. 177 (1968), 278–282. MR 225767, DOI 10.1007/BF01350720
  • Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 247 (1979), 125-136
  • MSC: Primary 13A15; Secondary 13C15, 13E05
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0517688-0
  • MathSciNet review: 517688