Acta Math Vietnam https://doi.org/10.1007/s40306-018-0271-2 El Hassane Fliouet Received: 14 April 2017 / Revised: 2 March 2018 / Accepted: 13 March 2018 © Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018 Abstract We describe the lower quasi-finite extensions K/k of characteristic p> 0, which −n are defined as follows: for every n ∈ N, k ∩ 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. Keywords Purely inseparable · Irrationality degree · Modular extension · q-finite extension · lq-finite extension · Absolutely lq-finite extension Mathematics Subject Classification (2010) 12F15 1 Introduction Let K/k be a purely inseparable extension of characteristic p> 0. We first introduce the size measurement of a purely inseparable extension by di(K/k) = sup (|B |) where B n n
Acta Mathematica Vietnamica – Springer Journals
Published: Jun 4, 2018
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