Direct Sum Decompositions of Torsion-Free Finite Rank Groups

Direct Sum Decompositions of Torsion-Free Finite Rank Groups examines advanced topics in the direct sum decompositions of abelian groups and their consequences. The book offers a unified approach to theoretic properties, covering isomorphism, endomorphism, refinement, the Baer splitting property, Gabriel filters, and endomorphism modules. The author makes extensive use of illustrative examples, with several open-ended examples serving as exercises at the end of each chapter to reinforce the concepts presented throughout the text. Useful appendices containing background material appear at the end of the book, making it an ideal research tool for mathematicians studying abelian 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 a group G by considering finitely generated projective right End(G)-modules, the left End(G)-module G, and the 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, and each rtffr L-group that is a J-group. The book concludes with useful appendices that contain background material and numerous examples.