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TitleStrongly Noetherian rings and constructive ideal theory
Author(s) Hervé Perdry
TypeArticle in Journal
AbstractWe give a new constructive definition for Noetherian rings. It has a very concrete statement and is nevertheless strong enough to prove constructively the termination of algorithms involving “trees of ideals”. The efficiency of such algorithms (at least for providing clear and intuitive constructive proofs) is illustrated in a section about Lasker–Noether rings: we give constructive proofs for the existence of the minimal primes over an ideal, of its radical, of its primary decomposition, in a wide class of polynomial rings.
KeywordsNoetherian ring
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717103001226
LanguageEnglish
JournalJournal of Symbolic Computation
Volume37
Number4
Pages511 - 535
Year2004
Edition0
Translation No
Refereed No
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