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Record Nr. |
UNINA9910818338603321 |
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Autore |
Alaca Saban <1964-> |
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Titolo |
Introductory algebraic number theory / / Saban Alaca, Kenneth S. Williams |
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Pubbl/distr/stampa |
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Cambridge ; ; New York, : Cambridge University Press, 2004 |
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ISBN |
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1-107-14885-5 |
0-511-79126-7 |
0-511-16609-5 |
0-511-16414-9 |
0-511-56680-8 |
0-511-16494-7 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (xvii, 428 pages) : digital, PDF file(s) |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Algebraic number theory |
Number theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
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Nota di bibliografia |
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Includes bibliographical references (p. 423-424) and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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