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On Stably Free Ideal Domains

Abstract : We define a stably free ideal domain to be a Noetherian domain whose left and right ideals ideals are all stably free. Every stably free ideal domain is a (possibly noncommutative) Dedekind domain, but the converse does not hold. The first Weyl algebra over a field of characteristic 0 is a typical example of stably free ideal domain. Some properties of these rings are studied. A ring is a principal ideal domain if, and only if it is both a stably free ideal domain and an Hermite ring.
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Contributor : Henri Bourlès <>
Submitted on : Wednesday, December 4, 2019 - 2:22:12 PM
Last modification on : Saturday, May 1, 2021 - 3:47:36 AM
Long-term archiving on: : Thursday, March 5, 2020 - 4:41:19 PM


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  • HAL Id : hal-02393572, version 1


Henri Bourlès. On Stably Free Ideal Domains. 2019. ⟨hal-02393572⟩



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