Finite Rank Torsion Free Abelian Groups and Rings

Inhaltsverzeichnis

• Notation and preliminaries.
• Types and rank—1 groups.
• Examples of indecomposable groups and direct sums.
• Endomorphism rings and decompositions of rank 2 groups.
• Pure subgroups of completely decomposable groups.
• Homogeneous completely decomposable groups and generalizations.
• Completely decomposable groups and generalizations.
• Additive categories, quasi-isomorphism and near-isomorphism.
• Stable range, substitution, cancellation, and exchange properties.
• Subrings of finite dimensional Q-algebras.
• Orders in finite dimensional simple Q-algebras.
• Maximal orders in finite dimensional simple Q-algebras.
• Near isomorphism and genus class.
• Grothendieck groups.
• Additive groups of subrings of finite dimensional Q-algebras.
• Q-simple and p-simple groups.