Algebraic Number Fields PDF Download
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| Author | : Gerald J. Janusz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 288 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821804294 |
Download Algebraic Number Fields Book in PDF, ePub and Kindle
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 |
Download The Theory of Algebraic Number Fields Book in PDF, ePub and Kindle
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 | : 203 |
| Release | : 2018-07-05 |
| Genre | : Mathematics |
| ISBN | : 3319902334 |
Download Number Fields Book in PDF, ePub and Kindle
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 |
Download The Genus Fields of Algebraic Number Fields Book in PDF, ePub and Kindle
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| Author | : Harvey Cohn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461299500 |
Download A Classical Invitation to Algebraic Numbers and Class Fields Book in PDF, ePub and Kindle
"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 | : 162 |
| Release | : 1975-12-31 |
| Genre | : Algebraic number theory |
| ISBN | : 1614440093 |
Download The Theory of Algebraic Numbers: Second Edition Book in PDF, ePub and Kindle
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 | : H. P. F. Swinnerton-Dyer |
| Publisher | : Cambridge University Press |
| Total Pages | : 164 |
| Release | : 2001-02-22 |
| Genre | : Mathematics |
| ISBN | : 9780521004237 |
Download A Brief Guide to Algebraic Number Theory Book in PDF, ePub and Kindle
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
| Author | : Edwin Weiss |
| Publisher | : Courier Corporation |
| Total Pages | : 308 |
| Release | : 2012-01-27 |
| Genre | : Mathematics |
| ISBN | : 048615436X |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
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.
| Author | : Paulo Ribenboim |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 676 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 0387216901 |
Download Classical Theory of Algebraic Numbers Book in PDF, ePub and Kindle
The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
| Author | : Frazer Jarvis |
| Publisher | : Springer |
| Total Pages | : 298 |
| Release | : 2014-06-23 |
| Genre | : Mathematics |
| ISBN | : 3319075454 |
Download Algebraic Number Theory Book in PDF, ePub and Kindle
This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.
