On n-dependent groups and fields

摘要

First, an example of a 2-dependent group without a minimal subgroup of bounded index is given. Second, all infinite n-dependent fields are shown to be Artin-Schreier closed. Furthermore, the theory of any non separably closed PAC field has the IPn property for all natural numbers n and certain properties of dependent (NIP) valued fields extend to the n-dependent context. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim