R. Göbel et al. (eds.), Abelian Group Theory © Springer-Verlag Berlin Heidelberg 1983 Page
1 ON PROJECTIVE nIMENSIONS OF MOnllLES OVER VALUATION nOMAINS L. Fuchs In this …

This book initiates a systematic, in-depth study of Modules Over Valuation Domains. It
introduces the theory of modules over commutative domains without finiteness conditions …

In [2] this was generalized to torsion free modules whose generator systems are of larger
cardinalities than their ranks. In [2] modules of projective dimension one are also studied …

This is the first in a series of papers deahng with the theory of modules over valuation rings.
It has been observed that a variety of concepts and basic results in abelian group theory can …

The first important extension of the theory of pure injective (ie algebraically compact) abelian
groups, developed in the'50's by Kaplansky [K], Łoś [L], Maranda [Mar] and others, to …

Introduction. A ring R is said to be of bounded module type if, for some positive integer n,
every finitely generated R-module is a direct sum of submodules generated by n elements …

Direct sum decompositions problems for torsion-free modules of finite rank have been the
subject of recent activity in the theory of modules over valuation domains (see eg [11]) …

This paper deals with the existence and uniqueness of direct sum decompositions of finitely
generated modules, and finite rank torsion-free modules, over valuation domains. In the first …

An equivalence is presented between two categories closely related to the category of
valuated vector spaces. This equivalence is then recast in terms of short exact sequences of …

1. Introduction and preliminaries. A left R-module M is called locally projective [10] if given
an epimorphismf: A-~ B, some 9 6 Hom (M, B) and a finitely generated submodule F of M …