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An example of a Hilbert ring with maximal ideals of different height


Author: Leslie G. Roberts
Journal: Proc. Amer. Math. Soc. 37 (1973), 425-426
MSC: Primary 13A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0313234-5
MathSciNet review: 0313234
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Abstract: An example is given of an integral domain which is a Hilbert ring of Krull dimension two but has some maximal ideals of height one.


References [Enhancements On Off] (What's this?)

  • [1] A. V. Geramita, Maximal ideals in polynomial rings over Dedekind domains, Queen's University Mathematical Preprint No. 1971-20. MR 0318123 (47:6672)
  • [2] I. Kaplansky, Commutative rings, Allyn & Bacon, Boston, Mass., 1970. MR 40 #7234. MR 0254021 (40:7234)
  • [3] W. Krull, Jacobsonsche Ringe, Hilbertscher Nullstellensatz, Dimensiontheorie, Math. Z. 54 (1951), 354-387. MR 13, 903. MR 0047622 (13:903c)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0313234-5
Article copyright: © Copyright 1973 American Mathematical Society

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