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Noetherian subsets of prime spectra

Authors: Charles C. Hanna and Jon L. Johnson
Journal: Proc. Amer. Math. Soc. 88 (1983), 397-398
MSC: Primary 13A17; Secondary 13B99
MathSciNet review: 699401
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Abstract: If $ X$ is a noetherian subspace of Spec $ R$, the set of primes of $ R[x]$ lying over $ X$ is also noetherian. A simple consequence is the theorem of Ohm and Pendleton that a ring module-finite over a $ j$-noetherian ring is $ j$-noetherian.

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

  • [1] I. Kaplansky, An introduction to differential algebra, Publ. Inst. Math. Univ. Nancago, Paris, 1957. MR 0093654 (20:177)
  • [2] J. Ohm and R. L. Pendleton, Rings with noetherian spectrum, Duke Math. J. 35 (1968), 631-640. MR 0229627 (37:5201)
  • [3] W. H. Raudenbush, Jr., Ideal theory and algebraic differential equations, Trans. Amer. Math. Soc. 36 (1934), 361-368. MR 1501748
  • [4] J. F. Ritt, Differential equations from the algebraic viewpoint, Amer. Math. Soc. Colloq. Publ., vol. 14, Amer. Math. Soc., Providence, R.I., 1932.

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Keywords: Prime spectrum, Noetherian spectrum
Article copyright: © Copyright 1983 American Mathematical Society

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