Direct Sum Decompositions of Torsion-Free Finite Rank Groups
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A01=Theodore G. Faticoni
abelian group theory
advanced group decomposition methods
Algebraic Number Field
algebraic structures
Author_Theodore G. Faticoni
Baer splitting property
Category=PBF
Category=PBG
Category=PBH
Commutative Ring
Corner's Theorem
Corner’s Theorem
dedekind
Dedekind Domain
Dedekind Group
Direct Sum Decompositions
Direct Summand
domain
e-module
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
exact
Finite Index
Finite Rank
finitely
generated
Idempotent Ideals
Indecomposable Decomposition
Integral Domain
Invertible Ideal
left
Left E-module
Locally Isomorphic
Maximal Ideal
module isomorphism
Orthogonal Idempotents
projective modules
Refinement Property
ring homomorphisms
rtffr
Rtffr Group
Semiperfect Ring
sequence
short
Short Exact Sequence
Torsion Free Group
Unique Decomposition
Unique Minimal Element
Units Modulo
Product details
- ISBN 9781584887263
- Weight: 566g
- Dimensions: 156 x 234mm
- Publication Date: 28 Mar 2007
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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.
Faticoni, Theodore G.
