Elementary Matrix-computational Proof of Quillen-Suslin Theorem for Ore Extensions

• Autorzy: Fajardo William , Lezama Oswaldo

Identyfikatory

DOI

10.3233/FI-2019-1754

• Języki publikacji: EN

Abstrakty

EN

In this short note we present an elementary matrix-constructive algorithmic proof of the Quillen-Suslin theorem for Ore extensions A := K[x; σ, δ], where K is a division ring, σ : K → K is a division ring automorphism and σ : K → K is a σ-derivation of K. It asserts that every finitely generated projective A-module is free. We construct a symbolic algorithm that computes the basis of a given finitely generated projective A-module. The algorithm is implemented in a computational package. Its efficiency is illustrated by four representative examples.

Słowa kluczowe

EN

maple; non-commutative computational algebra; ore extensions; projective modules; symbolic algorithms

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2019
• Tom: Vol. 164, nr 1
• Strony: 41--59
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Fajardo William

• Universidad Nacional de Colombia, Department of Mathematics, Bogot, Colombia

autor

Lezama Oswaldo

• Universidad Nacional de Colombia, Department of Mathematics, Bogot, Colombia

Bibliografia

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• [6] Lam, T.Y. Serre’s Problem on Projective Modules, Springer Monographs in Mathematics, Springer, 2006.
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• [10] Vasserstein LN, and Suslin AA. Serre’s problem on projective modules over polynomial rings, and algebraic K-theory, Funktional. Anal. i Prilozen. 1974;8(2):65-66.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).