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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https://hal.archives-ouvertes.fr/hal-02393572
Contributor : Henri Bourlès <>
Submitted on : Wednesday, December 4, 2019 - 2:22:12 PM
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Henri Bourlès. On Stably Free Ideal Domains. 2019. ⟨hal-02393572⟩

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