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Lazy bases: a minimalist constructive theory of Noetherian rings
Authors:Hervé Perdry
Institution:1. INSERM UMR‐S 535 and Université Paris‐Sud, F‐94817 Villejuif, France;2. The author now works in applied mathematics. This paper was conceived while attending a conference in Marrakech.
Abstract:We give a constructive treatment of the theory of Noetherian rings. We avoid the usual restriction to coherent rings; we can even deal with non‐discrete rings. We introduce the concept of rings with certifiable equality which covers discrete rings and much more. A ring R with certifiable equality can be fitted with a partial ideal membership test for ideals of R. Lazy bases of ideals of R X ] are introduced in order to derive a partial ideal membership test for ideals of R X ]. It is then proved that if R is Noetherian, then so is R X ]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Keywords:Constructive algebra  Noetherian rings  Hilbert basis theorem
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