Galois Theory Of P Extensions
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Galois Theory Of P Extensions
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Author : Helmut Koch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Galois Theory Of P Extensions written by Helmut Koch 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 2013-03-09 with Mathematics categories.
First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of pro-p groups and their cohomology, it discusses presentations of the Galois groups G S of maximal p-extensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to infinite class field towers.The book demonstrates that the cohomology of groups is very useful for studying Galois theory of number fields; at the same time, it offers a down to earth introduction to the cohomological method. In a "Postscript" Helmut Koch and Franz Lemmermeyer give a survey on the development of the field in the last 30 years. Also, a list of additional, recent references has been included.
Galois Theory Of P Extensions
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Author : Helmut Koch
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-08-06
Galois Theory Of P Extensions written by Helmut Koch 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 2002-08-06 with Mathematics categories.
Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.
Field Extensions And Galois Theory
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Author : Julio R. Bastida
language : en
Publisher: Cambridge University Press
Release Date : 1984-12-28
Field Extensions And Galois Theory written by Julio R. Bastida and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-28 with Mathematics categories.
This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.
Galois Theory Of P Extensions
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Author : Helmut Koch
language : en
Publisher: Springer
Release Date : 2012-12-22
Galois Theory Of P Extensions written by Helmut Koch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-22 with Mathematics categories.
Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.
Galois Theory And Modular Forms
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Author : Ki-ichiro Hashimoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Galois Theory And Modular Forms written by Ki-ichiro Hashimoto 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 2013-12-01 with Mathematics categories.
This volume is an outgrowth of the research project "The Inverse Ga lois Problem and its Application to Number Theory" which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No. 11440013. In September, 2001, an international conference "Galois Theory and Modular Forms" was held at Tokyo Metropolitan University after some preparatory work shops and symposia in previous years. The title of this book came from that of the conference, and the authors were participants of those meet All of the articles here were critically refereed by experts. Some of ings. these articles give well prepared surveys on branches of research areas, and many articles aim to bear the latest research results accompanied with carefully written expository introductions. When we started our re~earch project, we picked up three areas to investigate under the key word "Galois groups"; namely, "generic poly nomials" to be applied to number theory, "Galois coverings of algebraic curves" to study new type of representations of absolute Galois groups, and explicitly described "Shimura varieties" to understand well the Ga lois structures of some interesting polynomials including Brumer's sextic for the alternating group of degree 5. The topics of the articles in this volume are widely spread as a result. At a first glance, some readers may think this book somewhat unfocussed.
Field And Galois Theory
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Author : Patrick Morandi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Field And Galois Theory written by Patrick Morandi 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 the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have tojump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.
Topics In Galois Theory Second Edition
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Author : Jean-Pierre Serre
language : en
Publisher: A K Peters/CRC Press
Release Date : 2008
Topics In Galois Theory Second Edition written by Jean-Pierre Serre and has been published by A K Peters/CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for p-groups, p != 2, as well as Hilbert's irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of regular extensions of Q(T). While proofs are not carried out in full detail, the book contains a number of examples, exercises, and open problems.
Field Extensions And Galois Theory
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Author : Julio R. Bastida
language : en
Publisher: Cambridge University Press
Release Date : 1984-12-28
Field Extensions And Galois Theory written by Julio R. Bastida and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-28 with Mathematics categories.
This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.
Galois Theories
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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 2001-02-22
Galois Theories written by Francis Borceux and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-22 with Mathematics categories.
Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.
Galois Theory
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Author : Emil Artin
language : en
Publisher:
Release Date : 1946
Galois Theory written by Emil Artin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1946 with Galois theory categories.