Procyclic Galois Extensions of Algebraic Number Fields

David Brink

ISBN 10: 3838380045 / ISBN 13: 9783838380049

Published by LAP LAMBERT Academic Publishing Jul 2010, 2010

About this Item

Neuware -The main theme of this thesis is the existence and properties of Galois extensions of algebraic number fields with Galois group isomorphic to the additive group of p-adic integers, in short procyclic extensions. However, extensions with non-abelian pro-p-groups as Galois groups are also considered. The connection between procyclic extensions and Leopoldt''s Conjecture is discussed. The notion of p-rationality is defined, and the classification of 2-rational imaginary quadratic fields is given, apparently for the first time (correctly).Books on Demand GmbH, Überseering 33, 22297 Hamburg 96 pp. Englisch.

Seller Inventory # 9783838380049

Bibliographic Details

• Title: Procyclic Galois Extensions of Algebraic Number Fields
• Publisher: LAP LAMBERT Academic Publishing Jul 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 3838380045
• ISBN 13: 9783838380049
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 6D millimeters 220 millimeters width by 150 millimeters height by 6 millimeters depth
• Weight: 161 grams

About this title

Synopsis

The main theme of this thesis is the existence and properties of Galois extensions of algebraic number fields with Galois group isomorphic to the additive group of p-adic integers, in short procyclic extensions. However, extensions with non-abelian pro-p-groups as Galois groups are also considered. The connection between procyclic extensions and Leopoldt's Conjecture is discussed. The notion of p-rationality is defined, and the classification of 2-rational imaginary quadratic fields is given, apparently for the first time (correctly).

About the Author

David Brink received his Ph.D. from University of Copenhagen in 2006. Since then, he has held positions at Universidade de Brasília and University College Dublin. His research interests are number theory and combinatorics.