Representations of Posets and Indecomposable Torsion-Free Abelian Groups

Abstract

Representations of posets in certain modules are used to find indecomposable almost completely decomposable torsion-free abelian groups. For a special class of almost completely decomposable groups we determine the possible ranks of indecomposable groups and show that the possible ranks are realized by indecomposable groups in the class.

Key Words:

• Almost completely decomposable
• Indecomposable
• Representation

2010 Mathematics Subject Classification:

• Primary 20K15
• Secondary 20K25
• 16G60

Notes

Communicated by S. Bazzoni.