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A NOTE ON PRÜFER SEMISTAR MULTIPLICATION DOMAINS

  • Picozza, Giampaolo (UNIVERSITE PAUL CEZANNE AIX-MARSEILLE III LATP, FACULTE DES SCIENCES ET TECHNIQUES)
  • Published : 2009.11.01

Abstract

In this note we give a new generalization of the notions of $Pr{\ddot{U}}fer$ domain and PvMD which uses quasi semistar invertibility, the "quasi P$\star$MD", and compare them with the P$\star$MD. We show in particular that the problem of when a quasi P$\star$MD is a P$\star$MD is strictly related to the problem of the descent to subrings of the P$\star$MD property and we give necessary and sufficient conditions.

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