The Hierarchy of Uniserial Modules Over A Valuation Domain

The class of uniserial modules (i.e. modules whose submodules form a chain under inclusion) is studied over a valuation domain R. The isomorphy classes of torsion uniserial R-modules form a monoid Unis R under the operation Tor. In this paper, certain submonoids of Unis R are investigated, which consist of nonfinitely annihilated uniserials; these include all the nonstandard uniserial modules. Some of the submonoids turn out to be Clifford semigroups (i.e. unions of groups). Several results give information about the structure of monoids and about their group constituents. The non-finitely annihilated uniserials are classified into six classes; this classification is slightly different from the one for non-standard uniserials due to Bazzoni-Salce.