The notion of a valuated abelian group is introduced and various categorical properties are
studied. The pre-abelian category of p-local valuated groups provides an absolute setting for …

References Page 1 References [1] FW Anderson and KR Fuller, Rings and Categories of
Modules, SpringerVerlag, New York (1974). [2] VI Arnautov, ST Glavatsky, and AV Mikhalev …

. 1vl'l'={(a, b) laE A, b EB with (plXU= fJb} cc AJ> A IA o and fJ: BJ> B IBo are the canonical
homomorphisms and rp is an isomorphism of A IA o onto B IB o. It is sometimes more …

A global Warfield group is a summand of a simply presented abelian group. The theory of
global Warfield groups encompasses both the theory of totally projective $ p $-groups, which …

We introduce in this paper a class of Abelian groups which includes the torsion totally
projective groups and those torsion-free groups which are direct sums of groups of rank one …

Warfield studied p-local groups that are summands of simply presented groups, introducing
invariants that, together with Ulm invariants, determine these groups up to isomorphism. In …

Throughout, all modules will be Z-modules. p Of course, our use of is an automorphism. In
[15], Warfield studied the class of modules which arise as summands of simply presented …

All groups considered irt this paper re assumed to be additively written abelian groups. We
follow for the most part the notation and terminology of [2]. We mention the following …

This paper is a somewhat rewritten and shortened version of a paper first written many years
ago but never published. The paper introduces a class of modules over a discrete valuation …

1. Introduction. It is only within the last few years that research on mixed Abelian groups has
begun to be a major part of Abelian group theory. This paper is intended as an introduction …