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A NOTE ON PRÜFER SEMISTAR MULTIPLICATION DOMAINS
Picozza, Giampaolo Korean Mathematical Society 2009 대한수학회지 Vol.46 No.6
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.
A note on Prüfer semistar multiplication domains
Giampaolo Picozza 대한수학회 2009 대한수학회지 Vol.46 No.6
In this note we give a new generalization of the notions of Prüfer domain and PvMD which uses quasi semistar invertibility, the "quasi P*MD", and compare them with the P*MD. We show in particular that the problem of when a quasi P*MD is a P*MD is strictly related to the problem of the descent to subrings of the P*MD property and we give necessary and sufficient conditions.