Stably free modules over $\mathbf{R}[X]$ of rank $> \dim\mathbf{R}$ are free

DOI10.1090/S0025-5718-2010-02427-5zbMath1219.13006MaRDI QIDQ3168742

Ihsen Yengui

Publication date: 19 April 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

Quillen-Suslin theoremconstructive mathematicsHermite ringsstably free modulesHermite ring conjectureunimodular vectors

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Other constructive mathematics (03F65) Stability for projective modules (19A13) Stability for linear groups (19B14)

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Cites Work

• Generating non-Noetherian modules constructively
• Faisceaux algébriques cohérents
• A constructive comparison of the rings \(R(X)\) and \(R\langle X\rangle\) and application to the Lequain-Simis induction theorem
• The Hermite ring conjecture in dimension one
• The Bass-Quillen conjecture in dimension three but characteristic \(\neq 2,3\) via a question of A. Suslin
• Projective modules over R[\(X_ 1,\)\dots ,X//n, R a Prüfer domain]
• A course in constructive algebra
• Serre's conjecture
• An algorithm for unimodular completion over noetherian rings
• Making the use of maximal ideals constructive
• On Stably Extended Projective Modules Over Polynomial Rings
• Projective modules over polynomial rings
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