The theory of modules of separably closed fields 2

Pilar Dellunde, Françoise Delon, Françoise Point

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Abstract

In Dellunde et al. (J. Symbolic Logic 67(3) (2002) 997-1015), we determined the complete theory T e of modules of separably closed fields of characteristic p and imperfection degree e, e∈ω∪{∞}. Here, for 0≠e∈ω, we describe the closed set of the Ziegler spectrum corresponding to T e . Further, we establish a correspondence between certain submodules and n-types and we investigate several notions of dimensions and their relationships with the Lascar rank. Finally, we show that T e has uniform p.p. elimination of imaginaries and deduce uniform weak elimination of imaginaries. © 2004 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)181-210
JournalAnnals of Pure and Applied Logic
Volume129
Issue number1-3
DOIs
Publication statusPublished - 1 Oct 2004

Keywords

  • Dimensions
  • Modules
  • Separably closed fields
  • Skew polynomial rings
  • Types
  • Ziegler spectrum

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    Dellunde, P., Delon, F., & Point, F. (2004). The theory of modules of separably closed fields 2. Annals of Pure and Applied Logic, 129(1-3), 181-210. https://doi.org/10.1016/j.apal.2004.03.002