Arabian Journal of Mathematics

, Volume 7, Issue 4, pp 249–271 | Cite as

Pointwise minimal extensions

  • Paul-Jean Cahen
  • Gabriel Picavet
  • Martine Picavet-L’Hermitte
Open Access


We characterize pointwise minimal extensions of rings, introduced by Cahen et al. (Rocky Mt J Math 41:1081–1125, 2011), in the special context of domains. We show that pointwise minimal extensions are either integral or integrally closed. In the closed case, they are nothing but minimal extensions. Otherwise, there are four cases: either all minimal sub-extensions are of the same type (ramified, decomposed, or inert) or coexist as only ramified and inert minimal sub-extensions.

Mathematics Subject Classification

13B02 13B21 13B22 13B30 



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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Aix en ProvenceFrance
  2. 2.MathématiquesLe CendreFrance

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