The theory of modules of separably closed fields 2

In Dellunde et al. (J. Symbolic Logic 67(3) (2002) 997–1015), we determined the complete theory Te 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 Te. 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 Te has uniform p.p. elimination of imaginaries and deduce uniform weak elimination of imaginaries.