Introduction To The Theory Of Algebraic Numbers And Functions Theory Of Algebraic Numbers And Functions The
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Introduction To The Theory Of Algebraic Numbers And Fuctions
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Author :
language : en
Publisher: Academic Press
Release Date : 1966-01-01
Introduction To The Theory Of Algebraic Numbers And Fuctions written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966-01-01 with Mathematics categories.
Introduction to the Theory of Algebraic Numbers and Fuctions
Algebraic Numbers And Algebraic Functions
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Author : P.M. Cohn
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Algebraic Numbers And Algebraic Functions written by P.M. Cohn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
This book is an introduction to the theory of algebraic numbers and algebraic functions of one variable. The basic development is the same for both using E Artin's legant approach, via valuations. Number Theory is pursued as far as the unit theorem and the finiteness of the class number. In function theory the aim is the Abel-Jacobi theorem describing the devisor class group, with occasional geometrical asides to help understanding. Assuming only an undergraduate course in algebra, plus a little acquaintance with topology and complex function theory, the book serves as an introduction to more technical works in algebraic number theory, function theory or algebraic geometry by an exposition of the central themes in the subject.
The Theory Of Algebraic Numbers
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Author : Harry Pollard
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01
The Theory Of Algebraic Numbers written by Harry Pollard and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; Fermat conjecture. 1975 edition.
Lectures On The Theory Of Algebraic Numbers
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Author : E. T. Hecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Lectures On The Theory Of Algebraic Numbers written by E. T. Hecke 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.
. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.
Introduction To The Theory Of Algebraic Numbers And Fuctions
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Author : Martin Eichler
language : en
Publisher:
Release Date : 1966
Introduction To The Theory Of Algebraic Numbers And Fuctions written by Martin Eichler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Algebraic Number Fields
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Author :
language : en
Publisher: Academic Press
Release Date : 1973-08-15
Algebraic Number Fields written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-08-15 with Mathematics categories.
Algebraic Number Fields
An Invitation To Algebraic Numbers And Algebraic Functions
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Author : Franz Halter-Koch
language : en
Publisher: CRC Press
Release Date : 2020-05-04
An Invitation To Algebraic Numbers And Algebraic Functions written by Franz Halter-Koch and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-04 with Mathematics categories.
The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: • A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. • Several of the topics both in the number field and in the function field case were not presented before in this context. • Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).
Algebraic Numbers And Algebraic Functions
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Author : Emil Artin
language : en
Publisher: CRC Press
Release Date : 1967
Algebraic Numbers And Algebraic Functions written by Emil Artin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
Several Complex Variables With Connections To Algebraic Geometry And Lie Groups
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Author : Joseph L. Taylor
language : en
Publisher: American Mathematical Society
Release Date : 2025-03-21
Several Complex Variables With Connections To Algebraic Geometry And Lie Groups written by Joseph L. Taylor and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-21 with Mathematics categories.
This text presents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraic sheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest are the last three chapters, which are devoted to applications of the preceding material to the study of the structure and representations of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Mili?i?'s proof of the Borel-Weil-Bott theorem, which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for the expert.
A Course In Algebra
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Author : Ėrnest Borisovich Vinberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
A Course In Algebra written by Ėrnest Borisovich Vinberg 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 2003 with Mathematics categories.
Great book! The author's teaching experinece shows in every chapter. --Efim Zelmanov, University of California, San Diego Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It is plain that years of teaching abstract algebra have enabled him to say the right thing at the right time. --Irving Kaplansky, MSRI This is a comprehensive text on modern algebra written for advanced undergraduate and basic graduate algebra classes. The book is based on courses taught by the author at the Mechanics and Mathematics Department of Moscow State University and at the Mathematical College of the Independent University of Moscow. The unique feature of the book is that it contains almost no technically difficult proofs. Following his point of view on mathematics, the author tried, whenever possible, to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. Another important feature is that the book presents most of the topics on several levels, allowing the student to move smoothly from initial acquaintance to thorough study and deeper understanding of the subject. Presented are basic topics in algebra such as algebraic structures, linear algebra, polynomials, groups, as well as more advanced topics like affine and projective spaces, tensor algebra, Galois theory, Lie groups, associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. Written with extreme care and supplied with more than 200 exercises and 70 figures, the book is also an excellent text for independent study.