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Introductory algebraic number theory /

Alaca, Şaban, (1964-)

Introductory algebraic number theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512/.74
書名/作者:	Introductory algebraic number theory // Şaban Alaca, Kenneth S. Williams.
作者:	Alaca, Şaban,
其他作者:	Williams, Kenneth S.,
面頁冊數:	1 online resource (xvii, 428 pages) : : digital, PDF file(s).
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Algebraic number theory - Textbooks.
ISBN:	9780511791260 (ebook)
內容註:	Integral domains -- Euclidean domains -- Noetherian domains -- Elements integral over a domain -- Algebraic extensions of a field -- Algebraic number fields -- Integral bases -- Dedekind domains -- Norms of ideals -- Decomposing primes in a number field -- Units in real quadratic fields -- The ideal class group -- Dirichlet's unit theorem -- Applications to diophantine equations.
摘要、提要註:	Algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat's last theorem and which now has a wealth of applications to diophantine equations, cryptography, factoring, primality testing and public-key cryptosystems. This book provides an introduction to the subject suitable for senior undergraduates and beginning graduate students in mathematics. The material is presented in a straightforward, clear and elementary fashion, and the approach is hands on, with an explicit computational flavour. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested reading and to the biographies of mathematicians who have contributed to the development of algebraic number theory are given at the end of each chapter. There are over 320 exercises, an extensive index, and helpful location guides to theorems and lemmas in the text.
電子資源:	http://dx.doi.org/10.1017/CBO9780511791260

Introductory algebraic number theory /
Alaca, Şaban,1964-

Introductory algebraic number theory /Şaban Alaca, Kenneth S. Williams. - 1 online resource (xvii, 428 pages) :digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Integral domains -- Euclidean domains -- Noetherian domains -- Elements integral over a domain -- Algebraic extensions of a field -- Algebraic number fields -- Integral bases -- Dedekind domains -- Norms of ideals -- Decomposing primes in a number field -- Units in real quadratic fields -- The ideal class group -- Dirichlet's unit theorem -- Applications to diophantine equations.

Algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat's last theorem and which now has a wealth of applications to diophantine equations, cryptography, factoring, primality testing and public-key cryptosystems. This book provides an introduction to the subject suitable for senior undergraduates and beginning graduate students in mathematics. The material is presented in a straightforward, clear and elementary fashion, and the approach is hands on, with an explicit computational flavour. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested reading and to the biographies of mathematicians who have contributed to the development of algebraic number theory are given at the end of each chapter. There are over 320 exercises, an extensive index, and helpful location guides to theorems and lemmas in the text.

ISBN: 9780511791260 (ebook)Subjects--Topical Terms:

643817
Algebraic number theory
--Textbooks.

LC Class. No.: QA247 / .A43 2004

Dewey Class. No.: 512/.74

Introductory algebraic number theory /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Integral domains -- Euclidean domains -- Noetherian domains -- Elements integral over a domain -- Algebraic extensions of a field -- Algebraic number fields -- Integral bases -- Dedekind domains -- Norms of ideals -- Decomposing primes in a number field -- Units in real quadratic fields -- The ideal class group -- Dirichlet's unit theorem -- Applications to diophantine equations.
520 $a Algebraic number theory is a subject which came into being through the attempts of mathematicians to try to prove Fermat's last theorem and which now has a wealth of applications to diophantine equations, cryptography, factoring, primality testing and public-key cryptosystems. This book provides an introduction to the subject suitable for senior undergraduates and beginning graduate students in mathematics. The material is presented in a straightforward, clear and elementary fashion, and the approach is hands on, with an explicit computational flavour. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text. References to suggested reading and to the biographies of mathematicians who have contributed to the development of algebraic number theory are given at the end of each chapter. There are over 320 exercises, an extensive index, and helpful location guides to theorems and lemmas in the text.
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700 1 $a Williams, Kenneth S., $e author. $3 643816
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856 4 0 $u http://dx.doi.org/10.1017/CBO9780511791260

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