Valuated groups

AbstractThe 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 the relative homological algebra of balanced sequences of abelian groups. The torsion groups of dimension one in this category are precisely the totally projective groups. Investigations of projectives in the global category results in a natural homological setting for the stacked bases theorem. The category of subgroups of finitely generated groups, where maps are those that can be extended to the containing groups, is equivalent to a full exact subcategory of the category of valuated groups