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NOETHERIAN SPECTRUM ON RINGS AND MODULES

Published online by Cambridge University Press:  01 August 2011

DAVID E. RUSH
DAVID E. RUSH*
Affiliation:
Department of Mathematics, University of California, Riverside, CA 92521-0135, USA e-mail: [email protected]
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Abstract

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It is shown that the well-known characterizations of when a commutative ring R has Noetherian spectrum carry over to characterizations of when the set Spec(M) of prime submodules of a finitely generated module M is Noetherian. The symmetric algebra SR(M) of M is used to show that the Noetherian property of Spec(R), and some related properties, pass from the ring R to the finitely generated R-modules.

Keywords

13C9913E1513E99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 707 - 715
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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