Warfield modules are direct summands of simply presented Zp - modules, or, alternatively, are Zp - modules possessing a nice decomposition basis with simply presented cokernel. They have been classified up to isomorphism by theor Ilm-Kaplansky and Warfield invariants. Taking a model theoretic point of view and using infinitary languages we give here a complete theoretic characterization of a large class of Zp - modules having a nice decomposition basis. As a corollary, we obtain the classical classification of countable Warfield modules. This generalizes results by Barwise and Eklof.
Göbel, Rüdiger; Leistner, Katrin; Loth, Peter; and Strüngmann, Lutz, "Infinitary Equivalence of Zp- Modules with Nice Decomposition Bases" (2011). Mathematics Faculty Publications. 16.