Details:
Title  An algorithm for unimodular completion over Noetherian rings  Author(s)  Abdessalem Mnif, Ihsen Yengui  Type  Article in Journal  Abstract  We give an algorithm for the wellknown result asserting that if R is a polynomial ring in a finite number of variables over a Noetherian ring A of Krull dimension d < ∞ , then for n ⩾ 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 − y j ∈ A × for each i ≠ j . The most important guiding examples are affine rings K [ x 1 , … , x m ] / I and localizations of polynomial rings S −1 K [ x 1 , … , x m ] , with K an infinite field. Moreover, we give an algorithmic proof of Suslin  Keywords  Quillen–Suslin theorem, Suslin  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869307001421 
Language  English  Journal  Journal of Algebra  Volume  316  Number  2  Pages  483  498  Year  2007  Note  Computational Algebra  Edition  0  Translation 
No  Refereed 
No 
