A WEAKER FORM OF BAER'S SPLITTING PROBLEM OVER VALUATION DOMAINS

Abstract

Eklof-Fuchs [3] have shown that over an arbitrary valuation domain R, the modules B which satisfy Ext 1/R (B,T) = 0 for all torsion R-modules T are precisely the free R-modules. Here we modify the problem and describe all R-modules B for which Ext 1/R (B, T) vanishes for all bounded and for all divisible torsion R-modules T. It is well known that if R is a descrete rank one valuation domain then all torsion—free R-modules B have this property.