HOW TO USE ABELIAN GROUP THEORY FOR THE STUDY OF DIAGRAMS OVER LOCALLY WELL-ORDERED SETS

Abstract

The theory of abelian groups is exploited for the study of diagrams over locally well-ordered sets. This method yields a complete list of indecomposable diagrams as well as some direct decompositions into cyclics and a characterization of Σ-pure-injective diagrams. Moreover, we show the existence of stacked bases and give an analogue of a freeness criterion due to Griffith.