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On a New Class of Integral Domains with the Portable Property

  • David E. Dobbs
  • Gabriel Picavet
  • Martine Picavet-L’Hermitte
Chapter

Abstract

A (commutative integral) domain R is said to be a pseudo-almost divided domain if for all P ∈ Spec(R) and uPR P , there exists a positive integer n such that u n P. Such domains are related to several known kinds of domains, such as divided domains and straight domains. It is shown that “locally pseudo-almost divided” is a portable property of domains. Hence, if T is a domain with a maximal ideal Q and D is a subring of TQ, then the pullback \(R:= T \times _{T/Q}D\) is locally pseudo-almost divided if and only if both T and D are locally pseudo-almost divided. A similar pullback transfer result is given for the “straight domain” property (which is not known to be portable) by imposing additional restrictions on the data T, Q, D.

Keywords

Integral domain Pullback Portable property Straight domain Pseudo-almost divided domain PAVD APVD Almost Prüfer domain Divided domain Root closed 

Subject Classifications

[2010] Primary 13G05 Secondary 13A15 13F05 13B21 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • David E. Dobbs
    • 1
  • Gabriel Picavet
    • 2
  • Martine Picavet-L’Hermitte
    • 2
  1. 1.Department of MathematicsUniversity of TennesseeKnoxvilleUSA
  2. 2.Laboratoire de MathématiquesUniversité Blaise Pascal, UMR6620 CNRS, Les CézeauxAubière CedexFrance

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