Cotorsion theories cogenerated by N1-free abelian groups

Abstract

Given an N1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext (G, T) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructible universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exists some ugly N1-free abelian groups. © 2002 Rocky Mountain Mathematics Consortium.