Making the use of maximal ideals constructive

The purpose of this paper is to decipher constructively a lemma of Suslin which played a central role in his second solution of Serre's problem on projective modules over polynomial rings. This lemma says that for a commutative ring A if v1(X), . . . , vn(X) = A[X] where v1 is monic and n 3, then there exist 1, . . . , En-1(A[X]) such that, denoting by wi the first coordinate of i t(v2, . . . , vn), we have Res(v1, w1), . . . , Res(v1, w ) = A. By the constructive proof we give, Suslin's proof of Serre's problem becomes fully constructive. Moreover, the new method with which we treat this academic example may be a model for miming constructively proofs in which one works modulo each maximal ideal to prove that a given

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Ihsen Yengui
• Keywords: Central Role, Polynomial Rings, Projective Modules, TCS 2008, Theoretical Computer Science