Galois Module Structure
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Galois Module Structure
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Author : Victor Percy Snaith
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Galois Module Structure written by Victor Percy Snaith and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. This title addresses the Chinburg conjectures. It provides the background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions.
Galois Module Structure
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Author : Victor P. Snaith
language : en
Publisher:
Release Date : 2012
Galois Module Structure written by Victor P. Snaith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Galois modules (Algebra) categories.
Galois Module Structure Of Algebraic Integers
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Author : A. Fröhlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Galois Module Structure Of Algebraic Integers written by A. Fröhlich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In this volume we present a survey of the theory of Galois module structure for rings of algebraic integers. This theory has experienced a rapid growth in the last ten to twelve years, acquiring mathematical depth and significance and leading to new insights also in other branches of algebraic number theory. The decisive take-off point was the discovery of its connection with Artin L-functions. We shall concentrate on the topic which has been at the centre of this development, namely the global module structure for tame Galois extensions of numberfields -in other words of extensions with trivial local module structure. The basic problem can be stated in down to earth terms: the nature of the obstruction to the existence of a free basis over the integral group ring ("normal integral basis"). Here a definitive pattern of a theory has emerged, central problems have been solved, and a stage has clearly been reached when a systematic account has become both possible and desirable. Of course, the solution of one set of problems has led to new questions and it will be our aim also to discuss some of these. We hope to help the reader early on to an understanding of the basic structure of our theory and of its central theme, and to motivate at each successive stage the introduction of new concepts and new tools.
Multiplicative Galois Module Structure
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Author : A. Weiss
language : en
Publisher: American Mathematical Soc.
Release Date :
Multiplicative Galois Module Structure written by A. Weiss and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This text is the result of a short course on the Galois structure of S -units that was given at The Fields Institute in the autumn of 1993. Offering a new angle on an old problem, the main theme is that this structure should be determined by class field theory, in its cohomological form, and by the behaviour of Artin L -functions at s = 0. A proof of this - or even a precise formulation - is still far away, but the available evidence all points in this direction. The work brings together the current evidence that the Galois structure of S -units can be described. This is intended for graduate students and research mathematicians, specifically algebraic number theorists.
Galois Module Structure Of Algebraic Integers
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Author : Albrecht Fröhlich
language : en
Publisher: Springer
Release Date : 1983
Galois Module Structure Of Algebraic Integers written by Albrecht Fröhlich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Multiplicative Galois Module Structure
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Author : A. Weiss
language : en
Publisher:
Release Date : 2012
Multiplicative Galois Module Structure written by A. Weiss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Galois modules (Algebra) categories.
Hopf Algebras And Galois Module Theory
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Author : Lindsay N. Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-10
Hopf Algebras And Galois Module Theory written by Lindsay N. Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Education categories.
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Galois Module Structure In Wild Extensions Of The Rationale Function Field
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Author : Raymond Miller
language : en
Publisher:
Release Date : 1997
Galois Module Structure In Wild Extensions Of The Rationale Function Field written by Raymond Miller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Galois Theory Through Exercises
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Author : Juliusz Brzeziński
language : en
Publisher: Springer
Release Date : 2018-03-21
Galois Theory Through Exercises written by Juliusz Brzeziński and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.