Abelian Groups:
Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by pr...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Kent
Elsevier Science
2014
|
| Ausgabe: | 3rd ed |
| Schriftenreihe: | International Series in Pure and Applied Mathematics
v.12 |
| Schlagworte: | |
| Online-Zugang: | FAW01 |
| Zusammenfassung: | Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations.Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups.This book is intended for young research workers and students who intend to familiarize themselves with abelian groups |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 online resource (369 pages) |
| ISBN: | 9781483280905 9780080092065 |
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| 520 | |a Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations.Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups.This book is intended for young research workers and students who intend to familiarize themselves with abelian groups | ||
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Datensatz im Suchindex
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| author | Fuchs, L. |
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| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3rd ed |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:30:54Z |
| institution | BVB |
| isbn | 9781483280905 9780080092065 |
| language | English |
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| spelling | Fuchs, L. Verfasser aut Abelian Groups 3rd ed Kent Elsevier Science 2014 © 1960 1 online resource (369 pages) txt rdacontent c rdamedia cr rdacarrier International Series in Pure and Applied Mathematics v.12 Description based on publisher supplied metadata and other sources Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations.Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups.This book is intended for young research workers and students who intend to familiarize themselves with abelian groups Abelian groups Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Abelsche Gruppe (DE-588)4140988-7 s 1\p DE-604 Kahane, J. P. Sonstige oth Robertson, A. P. Sonstige oth Ulam, S. Sonstige oth Erscheint auch als Druck-Ausgabe Fuchs, L . Abelian Groups 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fuchs, L. Abelian Groups Abelian groups Abelsche Gruppe (DE-588)4140988-7 gnd |
| subject_GND | (DE-588)4140988-7 |
| title | Abelian Groups |
| title_auth | Abelian Groups |
| title_exact_search | Abelian Groups |
| title_full | Abelian Groups |
| title_fullStr | Abelian Groups |
| title_full_unstemmed | Abelian Groups |
| title_short | Abelian Groups |
| title_sort | abelian groups |
| topic | Abelian groups Abelsche Gruppe (DE-588)4140988-7 gnd |
| topic_facet | Abelian groups Abelsche Gruppe |
| work_keys_str_mv | AT fuchsl abeliangroups AT kahanejp abeliangroups AT robertsonap abeliangroups AT ulams abeliangroups |