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

摘要

Eklof-Fuchs 3 have shown that over an arbitrary valuation domainR, the modulesBwhich satisfy Ext 1/R (B,T) = 0 for all torsionR-modulesTare precisely the freeR-modules. Here we modify the problem and describe allR-modulesBfor which Ext 1/R (B, T) vanishes for all bounded and for all divisible torsionR-modulesT.It is well known that if R is a descrete rank one valuation domain then all torsion#x2014;freeR-modulesBhave this property.