Overrings as Intersections of Localizations of an Integral Domain

Abstract

Let D be an integral domain, X an indeterminate over D, and and c(g) _v  = D}, where c(g) is the ideal of D generated by the coefficients of g. Let R be an overring of D. In this paper, we study when R[X] _{N v} is flat over D[X] _{N v} and when D[X] _{N v} has the QR-property or QQR-property. For example, we show that D has the tQQR-property if and only if D[X] _{N v} has the QQR-property, if and only if D[X] has the tQQR-property.

Key Words:

• Star operation
• *-Flat
• *QR-Domain
• *QQR-Domain
• *-linked overring
• D[X] _{N *}

2010 Mathematics Subject Classification:

• 13A15
• 13G05
• 13F05

ACKNOWLEDGMENTS

The authors would like to thank the referee for several valuable comments and suggestions.

Notes

Communicated by F. Tartarone.

Dedicated to Marco Fontana on the occasion of his 65th birthday.