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Algebraic Number Fields


Algebraic Number Fields
Author: Gerald J. Janusz
Publisher: American Mathematical Soc.
ISBN: 0821804294
Size: 50.79 MB
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The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind domains, and valuations. The next two chapters discuss class field theory for number fields. The concluding chapter serves as an illustration of the concepts introduced in previous chapters. In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol. For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. It is also very suitable for independent study.




The Theory Of Algebraic Number Fields


Algebraic Number Fields
Author: David Hilbert
Publisher: Springer Science & Business Media
ISBN: 3662035456
Size: 11.62 MB
Format: PDF
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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.




Number Fields


Algebraic Number Fields
Author: Daniel A. Marcus
Publisher: Springer
ISBN: 3319902334
Size: 52.26 MB
Format: PDF, Docs
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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.




Algebraic Number Theory


Algebraic Number Fields
Author: Edwin Weiss
Publisher: Courier Corporation
ISBN: 9780486401898
Size: 10.32 MB
Format: PDF, Docs
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Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis). Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract techniques constitute the primary focus. Topics include introductory materials on elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields. Subjects correspond to those usually covered in a one-semester, graduate level course in algebraic number theory, making this book ideal either for classroom use or as a stimulating series of exercises for mathematically minded individuals.



Algebraic Number Fields
Language: en
Pages: 276
Authors: Gerald J. Janusz
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: American Mathematical Soc.
The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind
The Theory of Algebraic Number Fields
Language: en
Pages: 351
Authors: David Hilbert
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media
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
Analytic Arithmetic in Algebraic Number Fields
Language: en
Pages: 180
Authors: Baruch Z. Moroz
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer
Books about Analytic Arithmetic in Algebraic Number Fields
Number Fields
Language: en
Pages: 203
Authors: Daniel A. Marcus
Categories: Mathematics
Type: BOOK - Published: 2018-07-05 - Publisher: Springer
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
Galois Cohomology of Algebraic Number Fields
Language: en
Pages: 145
Authors: Klaus Haberland, Helmut Koch, Thomas Zink
Categories: Algebraic fields
Type: BOOK - Published: 1978 - Publisher:
Books about Galois Cohomology of Algebraic Number Fields