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Direct Sum Decompositions of Torsion-Free Finite Rank Groups (Paperback)
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Direct Sum Decompositions of Torsion-Free Finite Rank Groups (Paperback)
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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.
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