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Annali di Matematica Pura ed Applicata

, Volume 112, Issue 1, pp 285–304 | Cite as

Su una condizione di fattorialità debole e l’annullamento del gruppo di Picard

  • Grazia Tamone
Article

Summary

We give some characterizations of noetherian domains A such that « every irreducible element generates a primary ideal ». This condition, called (α)-property, is equivalent to the unique factorization if A is normal or a polynomial ring A=B[T]. If A is a1-dimensional k-algebra, the property (α) is equivalent to the vanishing of some Picard groups asPicA,Pic (A[T, T−1]),Pic (A|T|s), where S={Tn, n εZ}. We give not trivial examples of (α)-rings which aren’t factorial.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • Grazia Tamone
    • 1
  1. 1.Genova

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