Search

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]

Abstract: We constructively prove that for any ring R with Krull dimension ⩽d, the ring locally behaves like the ring or a localization of a polynomial ring of type with S a multiplicative subset of R such that the Krull dimension of is . As an application, we give a simple and constructive proof of the Lequain–Simis Induction Theorem which is an important variation of the Quillen Induction Theorem. [Copyright &y& Elsevier]