The theory of modules of separably closed fields 2

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.