Introduction. In the study of finitely generated modules over valuation domains, developed
by the authors in [4],[7] and [8], a relevant share has to be assigned to indecomposable …

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 …

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 …

The condition on a valuation domain h of being maximal, which goes back to Krull [8], and
the very close condition of being almost maximal, due to Kaplansky [7], were extensively …

INTRODUCTION. A valuation ring R is a commutative ring with 1, not necessarily a domain,
such that its ideals are linearly ordered by inclusion. Throughout, R will denote a valuation …

In what follows, B will denote a valuation domain, ie a com-mutative domain with 1 in which
the ideals form a chain under inclusion. We assume that 1~ is not equal to its field Q of …

This review paper is a continuation of two previous review papers devoted to properties of
modules over discrete valuation domains. The first part of this work was published in the …

A RESULT BY KULIKOV THAT DOES NOT EXTEND TO MODULES OVER GENERAL
VALUATION DOMAINS Page 1 proceedings of the american mathematical society Volume 111 …

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 …

A commutative ring R is said to be of bounded module type if there exists a positive integer n
such that every indecomposable finitely generated R-module can be generated by n …