Algebraic Number Fields
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Author | : Gerald J. Janusz |
Publisher | : American Mathematical Soc. |
Total Pages | : 288 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821804294 |
This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.
Author | : David Hilbert |
Publisher | : Springer Science & Business Media |
Total Pages | : 360 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662035456 |
A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Author | : Daniel A. Marcus |
Publisher | : Springer |
Total Pages | : 213 |
Release | : 2018-07-05 |
Genre | : Mathematics |
ISBN | : 3319902334 |
Requiring no more than a basic knowledge of abstract algebra, this text presents the mathematics of number fields in a straightforward, pedestrian manner. It therefore avoids local methods and presents proofs in a way that highlights the important parts of the arguments. Readers are assumed to be able to fill in the details, which in many places are left as exercises.
Author | : M. Ishida |
Publisher | : Springer |
Total Pages | : 123 |
Release | : 2006-12-08 |
Genre | : Mathematics |
ISBN | : 3540375538 |
Author | : Harvey Cohn |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461299500 |
"Artin's 1932 Göttingen Lectures on Class Field Theory" and "Connections between Algebrac Number Theory and Integral Matrices"
Author | : Harry Pollard |
Publisher | : American Mathematical Soc. |
Total Pages | : 175 |
Release | : 1975-12-31 |
Genre | : Mathematics |
ISBN | : 1614440093 |
This monograph makes available, in English, the elementary parts of classical algebraic number theory. This second edition follows closely the plan and style of the first edition. The principal changes are the correction of misprints, the expansion or simplification of some arguments, and the omission of the final chapter on units in order to make way for the introduction of some two hundred problems.
Author | : Paul Pollack |
Publisher | : American Mathematical Soc. |
Total Pages | : 329 |
Release | : 2017-08-01 |
Genre | : Mathematics |
ISBN | : 1470436531 |
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Author | : H. P. F. Swinnerton-Dyer |
Publisher | : Cambridge University Press |
Total Pages | : 164 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 9780521004237 |
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author | : Jürgen Neukirch |
Publisher | : Springer Science & Business Media |
Total Pages | : 831 |
Release | : 2013-09-26 |
Genre | : Mathematics |
ISBN | : 3540378898 |
This second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. In all it is a virtually complete treatment of a vast array of central topics in algebraic number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.
Author | : Edwin Weiss |
Publisher | : Courier Corporation |
Total Pages | : 308 |
Release | : 2012-01-27 |
Genre | : Mathematics |
ISBN | : 048615436X |
Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.