Direct Sum Decompositions of Torsion-Free Finite Rank Groups

By Theodore G. Faticoni

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 0367389320
• ISBN13: 9780367389321
• Release Date: September 2019
• Publisher: CRC Press
• Length: 344 Pages
• Weight: 0.55 lbs.
• Dimensions: 0.7" x 6.1" x 9.1"