Self-projective modules over valuation rings (Q788770)

Let R be a valuation domain. The valuation domains all of whose ideals are self-projective are characterized as the almost maximal valuation domains. Furthermore, it is shown that R is complete in its R-topology if and only if the quotient field of R is a self-projective R-module, which leads to a characterization of maximal valuation domains. In addition, the structure of self-projective torsion-free modules of finite rank over almost maximal valuation domains is given and several results on the self-projectivity of direct sums of uniserial modules over valuation domains were obtained.