S. K. Sehgal: An Introduction to Group Rings

Cover: 9781402002397 | An Introduction to Group Rings | S. K. Sehgal (u. a.) | Taschenbuch

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Beschreibung

to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton. Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-0239-7 ISBN 978-94-[...] (eBook) DOI 10.1007/978-94-[...] Printed an acid-free paper AII Rights Reserved © 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover Ist edition 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording Of by any information storage and retrieval system, without written permis sion from the copyright owner. Contents Preface ix 1 Groups 1 1.1 Basic Concepts . . . . . . . . . . . . 1 1.2 Homomorphisms and Factor Groups 10 1.3 Abelian Groups . 18 1.4 Group Actions, p-groups and Sylow Subgroups 21 1.5 Solvable and Nilpotent Groups 27 1.6 FC Groups .

Inhaltsverzeichnis

1 Groups.- 1.1 Basic Concepts.- 1.2 Homomorphisms and Factor Groups.- 1.3 Abelian Groups.- 1.4 Group Actions, p-groups and Sylow Subgroups.- 1.5 Solvable and Nilpotent Groups.- 1.6 FC Groups.- 1.7 Free Groups and Free Products.- 1.8 Hamiltonian Groups.- 1.9 The Hirsch Number.- 2 Rings, Modules and Algebras.- 2.1 Rings and Ideals.- 2.2 Modules and Algebras.- 2.3 Free Modules and Direct Sums.- 2.4 Finiteness Conditions.- 2.5 Semisimplicity.- 2.6 The Wedderburn-Artin Theorem.- 2.7 The Jacobson Radical.- 2.8 Rings of Algebraic Integers.- 2.9 Orders.- 2.10 Tensor Products.- 3 Group Rings.- 3.1 A Brief History.- 3.2 Basic Facts.- 3.3 Augmentation Ideals.- 3.4 Semisimplicity.- 3.5 Abelian Group Algebras.- 3.6 Some Commutative Subalgebras.- 4 A Glance at Group Representations.- 4.1 Definition and Examples.- 4.2 Representations and Modules.- 5 Group Characters.- 5.1 Basic Facts.- 5.2 Characters and Isomorphism Questions.- 6 Ideals in Group Rings.- 6.1 Ring Theoretic Formulas.- 6.2 Nilpotent Ideals.- 6.3 Nilpotent Augmentation Ideals.- 6.4 Semiprime Group Rings.- 6.5 Prime Group Rings.- 6.6 Chain Conditions in KG.- 7 Algebraic Elements.- 7.1 Introduction.- 7.2 Idempotent Elements.- 7.3 Torsion Units.- 7.4 Nilpotent Elements.- 8 Units of Group Rings.- 8.1 Introduction.- 8.2 Trivial Units.- 8.3 Finite Groups.- 8.4 Units of ZS3.- 8.5 Infinite Groups.- 8.6 Finite Generation of U(ZG).- 8.7 Central Units.- 9 The Isomorphism Problem.- 9.1 Introduction.- 9.2 The Normal Subgroup Correspondence.- 9.3 Metabelian Groups.- 9.4 Circle Groups.- 9.5 Further Results.- 9.6 The Modular Isomorphism Problem.- 10 Free Groups of Units.- 10.1 Free Groups.- 10.2 Free Groups of Units.- 10.3 Explicit Free Groups.- 10.4 Explicit Free Groups in H.- 11 Properties of the Unit Group.- 11.1 Integral Group Rings.- 11.2 Group Algebras.

Erscheinungsjahr:	2002
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Algebra and Applications
Inhalt:	xi 371 S.
ISBN-13:	9781402002397
ISBN-10:	1402002394
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Sehgal, S. K. Polcino Milies, César
Auflage:	Softcover reprint of the original 1st ed. 2002
Hersteller:	Springer Netherland Springer Netherlands Algebra and Applications
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 21 mm
Von/Mit:	S. K. Sehgal (u. a.)
Erscheinungsdatum:	28.02.2002
Gewicht:	0,581 kg

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