Article thumbnail
Location of Repository

Minimal modules over valuation domains

By B. Goldsmith and P. Zanardo


AbstractLet R be a valuation domain. We say that a torsion-free R-module is minimal if it is isomorphic to all its submodules of finite index. Here, the usual concept of finite index for groups is replaced by the more appropriate (for module theory) definition: a submodule H of the module G is said to be of finite index in G if the quotient G/H is a finitely presented torsion module. We investigate minimality in various settings and show inter alia that over a maximal valuation domain, all torsion-free modules are minimal. Constructions of non-minimal modules are given by utilizing realization theorems of May and the authors. We also show that direct sums of minimal modules may fail to be minimal

Publisher: Elsevier B.V.
Year: 2005
DOI identifier: 10.1016/j.jpaa.2004.11.009
OAI identifier:

Suggested articles

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.