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Finite Rank Torsion Free Abelian Groups and Rings

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Author(s): David M. Arnold (auth.)
Series: Lecture Notes in Mathematics 931
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1982

Language: English
Pages: 198
City: Berlin; New York
Tags: Group Theory and Generalizations

Notation and preliminaries....Pages 1-4
Types and rank—1 groups....Pages 5-20
Examples of indecomposable groups and direct sums....Pages 21-35
Endomorphism rings and decompositions of rank 2 groups....Pages 36-39
Pure subgroups of completely decomposable groups....Pages 40-46
Homogeneous completely decomposable groups and generalizations....Pages 47-57
Completely decomposable groups and generalizations....Pages 58-68
Additive categories, quasi-isomorphism and near-isomorphism....Pages 69-86
Stable range, substitution, cancellation, and exchange properties....Pages 87-107
Subrings of finite dimensional Q-algebras....Pages 108-118
Orders in finite dimensional simple Q-algebras....Pages 119-128
Maximal orders in finite dimensional simple Q-algebras....Pages 129-138
Near isomorphism and genus class....Pages 139-147
Grothendieck groups....Pages 148-159
Additive groups of subrings of finite dimensional Q-algebras....Pages 160-166
Q-simple and p-simple groups....Pages 167-177