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Noetherian orders

Published online by Cambridge University Press:  02 December 2010

HERVÉ PERDRY  and
PETER SCHUSTER
HERVÉ PERDRY
Affiliation:
Université Paris-Sud UMR-S 669 and Inserm U 669, 16 avenue Paul-Vaillant-Couturier, Bâtiment Inserm 15/16, Villejuif F-94807
PETER SCHUSTER
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England
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Abstract

Noether classes of posets arise in a natural way from the constructively meaningful variants of the notion of a Noetherian ring. Using an axiomatic characterisation of a Noether class, we prove that if a poset belongs to a Noether class, then so does the poset of the finite descending chains. When applied to the poset of finitely generated ideals of a ring, this helps towards a unified constructive proof of the Hilbert basis theorem for all Noether classes.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Issue 1 , February 2011 , pp. 111 - 124
Copyright
Copyright © Cambridge University Press 2010

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