Cotilting and a Hierarchy of Almost Cotorsion Groups

✍ Scribed by Rüdiger Göbel; Jan Trlifaj

• Book ID: 102575342
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 115 KB
• Volume: 224
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8103

✦ Synopsis

We describe the structure of all cotilting and partial cotilting groups, and of all cotilting torsion-free classes of groups. Under V s L, we also describe all tilting and partial tilting groups. As a by-product, we introduce new classes of groupsᎏcalled almost cotorsion groups. Unlike the well-known cotorsion groups, the almost cotorsion ones have a rather complex structure: we prove that any cotorsion free ring can be realized as an endomorphism ring of an almost cotorsion group.