A note on Pr\

Giampaolo Picozza

doi:10.4134/JKMS.2009.46.6.1179

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2009; 46(6): 1179-1192

Printed November 1, 2009

https://doi.org/10.4134/JKMS.2009.46.6.1179

A note on Pr\"ufer semistar multiplication domains

Giampaolo Picozza

Universit\'e Paul C\'ezanne Aix-Marseille III

Abstract

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Abstract

In this note we give a new generalization of the notions of Pr\"ufer domain and P$v$MD 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.

Keywords: semistar operation, star operation

MSC numbers: 13A15