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Unimodular rows over Laurent polynomial rings

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Abstract

We prove that for any ring R of Krull dimension not greater than 1 and n ⩾ 3, the group En (R[X, X−1]) acts transitively on Umn(R[X, X−1]). In particular, we obtain that for any ring R with Krull dimension not greater than 1, all finitely generated stably free modules over R[X, X−1] are free. All the obtained results are proved constructively.

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Authors and Affiliations

  1. Jamoum University College, Department of Mathematics, Umm Al-Qura University, P.O.Box 14035, Makkah Al-Mukarramah, 21955, Saudi Arabia

    Abdessalem Mnif

  2. IREM, Abdou Moumouni University, B.P. 10896, Niamey, Niger

    Morou Amidou

Authors
  1. Abdessalem Mnif
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  2. Morou Amidou
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Correspondence to Abdessalem Mnif.

Additional information

The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work Grant Code: 22UQU4331241DSR01.

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Mnif, A., Amidou, M. Unimodular rows over Laurent polynomial rings. Czech Math J 72, 927–934 (2022). https://doi.org/10.21136/CMJ.2022.0002-20

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  • DOI: https://doi.org/10.21136/CMJ.2022.0002-20

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