ISBN: 9781402002397 - an introduction to group rings (algebra and applications, 1, band 1) (3 Ergebnisse)

Zustand: New. In English.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

Zustand: New. Group rings play a central role in the theory of representations of groups and are very interesting algebraic objects in their own right. In their study, many branches of algebra come to an interplay. This book takes the reader from beginning to research level. It is suitable for mathematicians working in the area of group rings. Series: Algebras & Applications S. Num Pages: 371 pages, biography. BIC Classification: PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 240 x 160 x 20. Weight in Grams: 537. . 2002. Softcover reprint of the original 1st ed. 2002. Paperback. . . . . Books ship from the US and Ireland.…