Direct Sum Decompositions of Torsion-Free Finite Rank Groups Contributor(s): Faticoni, Theodore G. (Author) |
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ISBN: 0367389320 ISBN-13: 9780367389321 Publisher: CRC Press OUR PRICE: $75.95 Product Type: Paperback - Other Formats Published: September 2019 |
Additional Information |
BISAC Categories: - Mathematics | Algebra - General - Mathematics | Group Theory - Mathematics | Number Theory |
Dewey: 512.25 |
Series: Pure and Applied Mathematics |
Physical Information: 0.7" H x 6.1" W x 9.1" (0.55 lbs) 344 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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. |