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Un anneau de Prüfer

H. Lombardi (2010)

Actes des rencontres du CIRM

Let E be the ring of integer valued polynomials over . This ring is known to be a Prüfer domain. But it seems there does not exist an algorithm for inverting a nonzero finitely generated ideal of E . In this note we show how to obtain such an algorithm by deciphering a classical abstract proof that uses localisations of E at all prime ideals of E . This confirms a general program of deciphering abstract classical proofs in order to obtain algorithmic proofs.

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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