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On a New Class of Integral Domains with the Portable Property

In: Commutative Algebra

Author

Listed:
  • David E. Dobbs

    (University of Tennessee, Department of Mathematics)

  • Gabriel Picavet

    (Université Blaise Pascal, UMR6620 CNRS, Les Cézeaux, Laboratoire de Mathématiques)

  • Martine Picavet-L’Hermitte

    (Université Blaise Pascal, UMR6620 CNRS, Les Cézeaux, Laboratoire de Mathématiques)

Abstract

A (commutative integral) domain R is said to be a pseudo-almost divided domain if for all P ∈ Spec(R) and u ∈ PR 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 T∕Q, then the pullback R : = T × T ∕ Q D $$R:= T \times _{T/Q}D$$ 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.

Suggested Citation

  • David E. Dobbs & Gabriel Picavet & Martine Picavet-L’Hermitte, 2014. "On a New Class of Integral Domains with the Portable Property," Springer Books, in: Marco Fontana & Sophie Frisch & Sarah Glaz (ed.), Commutative Algebra, edition 127, pages 119-132, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0925-4_7
    DOI: 10.1007/978-1-4939-0925-4_7
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