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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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.


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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