``Modules of finite rank over Prüfer rings'' revisited (Q1125921)

The aim of the paper is to correct a gap in the argument of the author's paper: ``Modules of finite rank over Prüfer rings'' [Ann. Math., II. Ser. 65, 250-254 (1957; Zbl 0213.32002)]. This gap has been pointed out by \textit{L. Salce} and \textit{P. Zanardo} [in: Abelian group theory, Proc. Oberwolfach Conf. 1981, Lect. Notes Math. 874, 76-86 (1981; Zbl 0472.13004)] and bridged in the case of torsion free modules. The result which is proved here asserts that every finite rank module over an almost maximal valuation domain has its torsion module a direct summand which is a direct sum of uniserials (i.e., its submodules are totally ordered under inclusion). The whole module is such a direct sum if the torsion-free rank is one, if the torsion-free quotient is contained in a direct sum of cycles, or if the domain is maximal.