1. Making the use of maximal ideals constructive
- Author
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Yengui, Ihsen
- Subjects
- *
COMPUTATIONAL mathematics , *POLYNOMIAL rings , *COMMUTATIVE rings , *MODULES (Algebra) , *PROJECTIVE modules (Algebra) , *FINITE groups - Abstract
Abstract: 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 if where is monic and , then there exist such that, denoting by the first coordinate of , we have . 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 abstract proofs in which one works modulo a generic maximal ideal in order to prove that an ideal contains 1. [Copyright &y& Elsevier]
- Published
- 2008
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