# Pointwise minimal extensions

Arabian Journal of Mathematics, Mar 2018

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.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs40065-018-0202-z.pdf

Paul-Jean Cahen, Gabriel Picavet, Martine Picavet-L’Hermitte. Pointwise minimal extensions, Arabian Journal of Mathematics, 2018, 1-23, DOI: 10.1007/s40065-018-0202-z