Acta Mathematica Vietnamica

, Volume 44, Issue 3, pp 751–779 | Cite as

Absolutely lq-Finite Extensions

  • El Hassane FliouetEmail author


We describe the lower quasi-finite extensions \(K/k\) of characteristic \(p>0\), which are defined as follows: for every \(n\in \mathbb N, k^{p^{-n}} \cap K/k \) is finite. We are especially interested in examining the absolute case. In this regard, we give necessary and sufficient condition for an absolutely lq-finite extension to be of finite size. Moreover, we show that any extension that is at the same time modular and lq-finite is of finite size. Furthermore, we construct an example of extension \(K/k\) of infinite size such that for any intermediate field L of \(K/k, L\) is of finite size over k.


Purely inseparable Irrationality degree Modular extension q-finite extension lq-finite extension Absolutely lq-finite extension 

Mathematics Subject Classification (2010)




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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Regional Center for the Professions of Education and TrainingAgadirMorocco

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