Equimorphism classes of uniserial modules over valuation domains (Q750532)

A module is called uniserial if its submodules form a chain. Two uniserial modules are called equimorphic if they are quotients of each other. In this paper equimorphism classes of uniserial modules over a valuation domain R are investigated, with particular regard to non- standard uniserial modules, i.e. those uniserials which are not isomorphic to quotients of submodules of the field of quotients of R. Some new results on the classes \(U_ 5\) and \(U_ 6\) of non-standard uniserials, introduced by the authors in a previous paper [``Elongations of uniserial modules over valuation domains'' (to appear in J. Algebra), are also obtained. [See also Zbl 0714.13008.]