Theory Of Algebraic Functions Of One Variable
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Author |
: Claude Chevalley |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 204 |
Release |
: 1951-12-31 |
ISBN-10 |
: 9780821815069 |
ISBN-13 |
: 0821815067 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Introduction to the Theory of Algebraic Functions of One Variable by : Claude Chevalley
Presents an approach to algebraic geometry of curves that is treated as the theory of algebraic functions on the curve. This book discusses such topics as the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, and extensions of the fields of functions (covering theory) and of the fields of constants.
Author |
: Max Deuring |
Publisher |
: Springer |
Total Pages |
: 157 |
Release |
: 2006-11-15 |
ISBN-10 |
: 9783540383680 |
ISBN-13 |
: 3540383689 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Lectures on the Theory of Algebraic Functions of One Variable by : Max Deuring
Author |
: Gabriel Daniel Villa Salvador |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 658 |
Release |
: 2007-10-10 |
ISBN-10 |
: 9780817645151 |
ISBN-13 |
: 0817645152 |
Rating |
: 4/5 (51 Downloads) |
Synopsis Topics in the Theory of Algebraic Function Fields by : Gabriel Daniel Villa Salvador
The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.
Author |
: Richard Dedekind |
Publisher |
: American Mathematical Society(RI) |
Total Pages |
: 0 |
Release |
: 2012 |
ISBN-10 |
: 0821883305 |
ISBN-13 |
: 9780821883303 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Theory of Algebraic Functions of One Variable by : Richard Dedekind
The 1882 Theorie der algebraischen Functionen einer Veränderlichen by Dedekind (1831-1916) and Weber (1842-1913) changed the direction of algebraic geometry and established its foundations by introducing methods from algebraic number theory. They used rings and ideals to give rigorous proofs of results that had previously been obtained in non-rigorous fashion, with the help of analysis and topology. Stillwell (mathematics, U. of San Francisco) believes that the paper still has gems for modern mathematicians that the standard commentaries do not mention. He presents the first English translation of it and provides commentary to the language and thinking of mathematics during the 19th century. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Author |
: Richard Dedekind |
Publisher |
: American Mathematical Society(RI) |
Total Pages |
: 0 |
Release |
: 2012 |
ISBN-10 |
: 0821883305 |
ISBN-13 |
: 9780821883303 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Theory of Algebraic Functions of One Variable by : Richard Dedekind
The 1882 Theorie der algebraischen Functionen einer Veränderlichen by Dedekind (1831-1916) and Weber (1842-1913) changed the direction of algebraic geometry and established its foundations by introducing methods from algebraic number theory. They used rings and ideals to give rigorous proofs of results that had previously been obtained in non-rigorous fashion, with the help of analysis and topology. Stillwell (mathematics, U. of San Francisco) believes that the paper still has gems for modern mathematicians that the standard commentaries do not mention. He presents the first English translation of it and provides commentary to the language and thinking of mathematics during the 19th century. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Author |
: P.M. Cohn |
Publisher |
: CRC Press |
Total Pages |
: 208 |
Release |
: 1991-09-01 |
ISBN-10 |
: 0412361906 |
ISBN-13 |
: 9780412361906 |
Rating |
: 4/5 (06 Downloads) |
Synopsis Algebraic Numbers and Algebraic Functions by : P.M. Cohn
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.
Author |
: Henning Stichtenoth |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 360 |
Release |
: 2009-02-11 |
ISBN-10 |
: 9783540768784 |
ISBN-13 |
: 3540768785 |
Rating |
: 4/5 (84 Downloads) |
Synopsis Algebraic Function Fields and Codes by : Henning Stichtenoth
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
Author |
: Helmut Koch |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 390 |
Release |
: 2000 |
ISBN-10 |
: 0821820540 |
ISBN-13 |
: 9780821820544 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Number Theory by : Helmut Koch
Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.
Author |
: Emil Artin |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 366 |
Release |
: 2005 |
ISBN-10 |
: 9780821840757 |
ISBN-13 |
: 0821840754 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Algebraic Numbers and Algebraic Functions by : Emil Artin
Originated from the notes of a course given at Princeton University in 1950-1951, this text offers an introduction to algebraic numbers and algebraic functions. It starts with the general theory of valuation fields, proceeds to the local class field theory, and then to the theory of function fields in one variable.
Author |
: Etienne Bézout |
Publisher |
: Princeton University Press |
Total Pages |
: 363 |
Release |
: 2009-01-10 |
ISBN-10 |
: 9781400826964 |
ISBN-13 |
: 1400826969 |
Rating |
: 4/5 (64 Downloads) |
Synopsis General Theory of Algebraic Equations by : Etienne Bézout
This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.