Direct Sum Decompositions of Torsion-Free Finite Rank Groups

Theodore G. Faticoni

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English

Chapman & Hall/CRC
19 September 2019

Groups & group theory

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.

By: Theodore G. Faticoni
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9780367389321
ISBN 10: 0367389320
Pages: 344
Publication Date: 19 September 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Faticoni, Theodore G.