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

DOI:
https://doi.org/10.1090/S0002-9939-1983-0699401-6

MathSciNet review:
699401

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Abstract: If is a noetherian subspace of Spec , the set of primes of lying over is also noetherian. A simple consequence is the theorem of Ohm and Pendleton that a ring module-finite over a -noetherian ring is -noetherian.

**[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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DOI:
https://doi.org/10.1090/S0002-9939-1983-0699401-6

Keywords:
Prime spectrum,
Noetherian spectrum

Article copyright:
© Copyright 1983
American Mathematical Society