Noetherian subsets of prime spectra
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- by Charles C. Hanna and Jon L. Johnson PDF
- Proc. Amer. Math. Soc. 88 (1983), 397-398 Request permission
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
- Irving Kaplansky, An introduction to differential algebra, Publ. Inst. Math. Univ. Nancago, No. 5, Hermann, Paris, 1957. MR 0093654
- Jack Ohm and R. L. Pendleton, Rings with noetherian spectrum, Duke Math. J. 35 (1968), 631–639. MR 229627
- H. W. Raudenbush Jr., Ideal theory and algebraic differential equations, Trans. Amer. Math. Soc. 36 (1934), no. 2, 361–368. MR 1501748, DOI 10.1090/S0002-9947-1934-1501748-1 J. F. Ritt, Differential equations from the algebraic viewpoint, Amer. Math. Soc. Colloq. Publ., vol. 14, Amer. Math. Soc., Providence, R.I., 1932.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 397-398
- MSC: Primary 13A17; Secondary 13B99
- DOI: https://doi.org/10.1090/S0002-9939-1983-0699401-6
- MathSciNet review: 699401