Arabian Journal of Mathematics

, Volume 7, Issue 4, pp 249–271

# Pointwise minimal extensions

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

## Abstract

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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