ℵn-FREE MODULES OVER COMPLETE DISCRETE VALUATION DOMAINS WITH ALMOST TRIVIAL DUAL

אn-Free Modules With Trivial Duals

In the first part of this paper we introduce a simplified version of a new Black Box from Shelah [11] which can be used to construct complicated אn-free abelian groups for any natural number n ∈ N. In the second part we apply this prediction principle to derive for many commutative rings R the existence of אn-free R-modules M with trivial dual M ∗ = 0, where M∗ = Hom(M, R). The minimal size of ...

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.

A Classification of Modules over Complete Discrete Valuation Rings

Dual Modules over a Valuation

Divisible Uniserial Modules over Valuation Domains