A classification of modules over complete discrete valuation rings

A Classification of Modules over Complete Discrete Valuation Rings

Localization of Injective Modules over Valuation Rings

It is proved that EJ is injective if E is an injective module over a valuation ring R, for each prime ideal J 6= Z. Moreover, if E or Z is flat, then EZ is injective too. It follows that localizations of injective modules over h-local Prüfer domains are injective too. If S is a multiplicative subset of a noetherian ring R, it is well known that SE is injective for each injective R-module E. The...

On Ramified Complete Discrete Valuation Rings

Injective Modules and Fp-injective Modules over Valuation Rings

It is shown that each almost maximal valuation ring R, such that every indecomposable injective R-module is countably generated, satisfies the following condition (C): each fp-injective R-module is locally injective. The converse holds if R is a domain. Moreover, it is proved that a valuation ring R that satisfies this condition (C) is almost maximal. The converse holds if Spec(R) is countable....

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.