Direct Sum Decompositions of Torsion-Free Finite Rank Groups

With plenty of new material not found in other books, "Direct Sum Decompositions of Torsion-Free Finite Rank Groups" explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups. Offering a unified approach to theoretic concepts, this reference covers isomorphism, endomorphism, refinement, the Baer splitting property, Gabriel filters, and endomorphism modules. It shows how to effectively study group G by considering finitely generated projective right End(G)-modules, left End(G)-module G, and ring E(G) = End(G)/N(End(G)). For instance, one of the naturally occurring properties considered is when E(G) is a commutative ring. Modern algebraic number theory provides results concerning the isomorphism of locally isomorphic rtffr groups, finitely faithful S-groups that are J-groups most of the time, and each rtffr L-group that is a J-group. The book concludes with useful appendices that contain background material and numerous examples.