Partial Decomposition Bases and Warfield Modules

Abstract

We consider the class of ℤ_p -modules with partial decomposition bases. This class was developed in order to extend Barwise and Eklof's classification of torsion groups in L _∞ω to Warfield modules. We prove that this class is the natural generalization of Warfield modules in L _∞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.

Key Words:

• k-modules
• Moore modules
• Partial decomposition basis
• Partial isomorphism
• Warfield modules

2010 Mathematics Subject Classification:

• Primary 03C52
• 13C05
• Secondary 20K21
• 03E10
• 20K25

Notes

Communicated by S. Bazzoni.