Partial Decomposition Bases and Warfield Modules
We consider the class ofℤp-modules with partial decomposition bases. This class was developed in order to extend Barwise and Eklof's classification of torsion groups inL∞ωto Warfield modules. We prove that this class is the natural generalization of Warfield modules inL∞ω, is strictly larger than the class of Warfield modules, and in fact strictly larger than the class of modules partially isomorphic to Warfield modules. We prove that this class is identical to the class of k-modules of Hill and Megibben, and, as such, closed under direct summands.
Jacoby, Carol and Peter Loth. "Partial Decomposition Bases and Warfield Modules." Communications in Algebra 42.10 (2014): 4333-4349.