On \(n\)-dependent groups and fields (Q2813675)
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scientific article; zbMATH DE number 6598143
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(n\)-dependent groups and fields |
scientific article; zbMATH DE number 6598143 |
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24 June 2016
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\(n\)-dependent groups
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\(n\)-dependent fields
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On \(n\)-dependent groups and fields (English)
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\(n\)-dependent, or NIP\(_n\), theories are a generalization of NIP theories introduced by \textit{S. Shelah} [Isr. J. Math. 204, 1--83 (2014; Zbl 1371.03043)]. This article studies algebraic examples of theories which are \(n\)-dependent. In particular, a \(2\)-dependent group that is not NIP is constructed, giving the first non-combinatorial example of such an object. Also, some results from NIP group and field theory are extended to the NIP\(_n\) context. For example \(n\)-dependent fields are shown to be Artin-Schreier closed, generalizing a result of \textit{I. Kaplan} et al. [Isr. J. Math. 185, 141--153 (2011; Zbl 1261.03120)].
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