Direct Sum Decompositions of Torsion-Free Finite Rank Groups

1. Auflage 2019
ISBN: 978-0-367-38932-1
Verlag: Chapman and Hall/CRC

Buch, Englisch, 344 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 518 g

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.

Zielgruppe

Professional Practice & Development

Autoren/Hrsg.

Faticoni, Theodore G.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

Abstract. Notation and Preliminary Results. Motivation by Example. Local Isomorphism is Isomorphism. Commuting Engomorphisms. Refinement Revisited. The Baer Splitting Property. J-groups, L-groups, and S-groups. Gabriel Filters. Endomorphism Modules. Appendices. Bibliography. Index.

Über Autor(innen)

Faticoni, Theodore G.