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Unimodular rows over Laurent polynomial rings

Abdessalem Mnif, Morou Amidou (2022)

Czechoslovak Mathematical Journal

We prove that for any ring 𝐑 of Krull dimension not greater than 1 and n 3 , the group E n ( 𝐑 [ X , X - 1 ] ) acts transitively on Um n ( 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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