On Stably Extended Projective Modules Over Polynomial Rings

DOI10.2307/2045909zbMath0595.13009OpenAlexW4252289083MaRDI QIDQ3726229

Moshe Roitman

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2045909

zbMATH Keywords

noetherian ringprojective module over polynomial ring

Mathematics Subject Classification ID

Projective and free modules and ideals in commutative rings (13C10) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Extension theory of commutative rings (13B02)

Related Items (25)

\(K_0\)-stability over monoid algebras ⋮ Stably free modules over $\mathbf{R}[X$ of rank $> \dim\mathbf{R}$ are free] ⋮ Two examples of the Bass-Quillen-Suslin conjectures ⋮ On Completing Unimodular Polynomial Vectors of Length Three ⋮ The Bass-Quillen conjecture in dimension three but characteristic \(\neq 2,3\) via a question of A. Suslin ⋮ Quillen–Suslin theory for the special linear group ⋮ A sufficient criterion about group homomorphism of the first row map ⋮ On the existence of unimodular elements and cancellation of projective modules over noetherian and non-noetherian rings ⋮ A note on relative Vaserstein symbol ⋮ On completion of unimodular rows over polynomial extension of finitely generated rings over \(\mathbb{Z}\) ⋮ A Study of Suslin Matrices: Their Properties and Uses ⋮ On the action of the elementary group on the unimodular rows ⋮ Two Approaches to the Bass–Suslin Conjecture ⋮ Unnamed Item ⋮ Non-self-dual Stably Free Modules ⋮ The Hermite ring conjecture in dimension one ⋮ A nice group structure on the orbit space of unimodular rows ⋮ A Fundamental Property of Suslin Matrices ⋮ A group structure on squares ⋮ On the first row map \(\mathrm{GL}_{d+1}(R)\longrightarrow\frac{Um_{d+1}(R)}{E_{d+1}(R)}\) ⋮ Quillen-Suslin theory revisited ⋮ A stably elementary homotopy ⋮ On stably free modules over Laurent polynomial rings ⋮ On a question of Moshe Roitman and Euler class of stably free module ⋮ Unimodular rows over Laurent polynomial rings

Cites Work

• Unnamed Item
• Unnamed Item
• Operations on orbits of unimodular vectors
• On the Bass-Quillen conjecture concerning projective modules over polynomial rings
• Projektive Moduln über Polynomringen \(A[T_1,\dots,T_M\) mit einem regulären Grundring \(A\)
• Serre's conjecture
• [https://portal.mardi4nfdi.de/wiki/Publication:3712413 On Projective R f 1 � f t -Modules]
• ON STABLY FREE MODULES
• Projective Modules over Laurent Polynomial Rings
• On Unimodular Rows
• Projective modules over polynomial rings

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