On non-standard uniserial modules over valuation domains and their quotients

Divisible Uniserial Modules over Valuation Domains

Explicitly Non-Standard Uniserial Modules

A new construction is given of non-standard uniserial modules over certain valuation domains; the construction resembles that of a special Aronszajn tree in set theory. A consequence is the proof of a sufficient condition for the existence of non-standard uniserial modules; this is a theorem of ZFC which complements an earlier independence result.

On a Conjecture regarding Non-standard Uniserial Modules

We consider the question of which valuation domains (of cardinality א1) have nonstandard uniserial modules. We show that a criterion conjectured by Osofsky is independent of ZFC + GCH. 1991 Mathematics Subject Classification. Primary 13L05, 03E35, 13C05; Secondary 03E75, 13A18.

Filtered Modules over Discrete Valuation Domains

We consider a uni ed setting for studying local valuated groups and coset-valuated groups, emphasizing the associated ltrations rather than the values of elements. Stable exact sequences, projectives and injectives are identi ed in the encompassing category, and in the category corresponding to coset-valuated groups.

Sigma-cotorsion Modules over Valuation Domains

We give a characterization of Σ-cotorsion modules over valuation domains in terms of descending chain conditions on certain chains of definable subgroups. We prove that pure submodules, direct products and modules elementarily equivalent to a Σ-cotorsion module are again Σ-cotorsion. Moreover, we describe the structure of Σ-cotorsion modules.