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TitleAn algorithm for unimodular completion over Noetherian rings
Author(s) Abdessalem Mnif, Ihsen Yengui
TypeArticle in Journal
AbstractWe give an algorithm for the well-known result asserting that if R is a polynomial ring in a finite number of variables over a Noetherian ring A of Krull dimension d < &#8734; , then for n &#10878; max ( 3 , d + 2 ) , SL n ( R ) acts transitively on Um n ( R ) . For technical reasons we demand that the Noetherian ring A has a theory of Gröbner bases and contains an infinite set E = y 1 , y 2 , … such that y i &#8722; y j &#8712; A × for each i &#8800; j . The most important guiding examples are affine rings K [ x 1 , … , x m ] / I and localizations of polynomial rings S &#8722;1 K [ x 1 , … , x m ] , with K an infinite field. Moreover, we give an algorithmic proof of Suslin
KeywordsQuillen–Suslin theorem, Suslin
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869307001421
LanguageEnglish
JournalJournal of Algebra
Volume316
Number2
Pages483 - 498
Year2007
NoteComputational Algebra
Edition0
Translation No
Refereed No
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