Units in Skew Fields
Published on 29. October 2012
Book
Paperback/Softback
VIII, 80 pages
978-3-0348-9555-2 (ISBN)
Description
This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.
More details
Series
Edition
Softcover reprint of the original 1st ed. 2000
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
VIII, 80 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 6 mm
Weight
154 gr
ISBN-13
978-3-0348-9555-2 (9783034895552)
DOI
10.1007/978-3-0348-8409-9
Schweitzer Classification
Other editions
Additional editions
Ernst Kleinert
Units in Skew Fields
Book
04/2000
1st Edition
Springer
€85.55
Article exhausted; check different version
Person
Dr. Ernst Kleinert lehrt Zahlentheorie an der Universität Hamburg.
Content
0 Basic Facts.- 1 Hey's Theorem and Consequences.- 2 Siegel-Weyl Reduction Theory.- 3 The Tamagawa Number and the Volume of G(?)/G(?).- 3.1 Statement of the main result.- 3.2 Proof of 3.1.- 3.3 The volume of G(?)/G(?).- 4 The Size of ?.- 4.1 Statement of results.- 4.2 Proofs.- 5 Margulis' Finiteness Theorem.- 5.1 The Result.- 5.2 Amenable groups.- 5.3 Kazhdan's property (T).- 5.4 Proof of 5.1; beginning.- 5.5 Interlude: parabolics and their opposites.- 5.6 Continuation of the proof.- 5.7 Contracting automorphisms and the Moore Ergodicity theorem.- 5.8 End of proof.- 5.9 Appendix on measure theory.- 6 A Zariski Dense and a Free Subgroup of ?.- 7 An Example.- 8 Problems.- 8.1 Generators.- 8.2 The congruence problem.- 8.3 Betti numbers.- References.