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# Introductory Algebraic Number Theory

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Published by Cambridge University Press .
Written in English

### Subjects:

• Algebraic number theory,
• Number Theory,
• Mathematics,
• Science/Mathematics,
• Mathematics / Number Theory,
• Textbooks

## Book details:

The Physical Object
FormatPaperback
Number of Pages446
ID Numbers
Open LibraryOL7745441M
ISBN 100521540119
ISBN 109780521540117

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Introductory Algebraic Number Theory. Suitable for senior undergraduates and beginning graduate students in mathematics, this book is an introduction to algebraic number theory at an elementary level. Prerequisites are kept to a minimum, and numerous examples illustrating the material occur throughout the text/5. 'This book provides a nice introduction to classical parts of algebraic number theory. The text is written in a lively style and can be read without any prerequisites. Therefore the book is very suitable for graduate students starting mathematics courses or mathematicians interested in introductory reading in algebraic number by: INTRODUCTORY ALGEBRAIC NUMBER THEORY Algebraic number theory is a subject that came into being through the attempts of mathe-maticians to try to prove Fermat’s last theorem and that now has a wealth of applications to Diophantine equations, cryptography, . This book is a genetic introduciton to algebraic number theory which follows the development of the subject in the work of Fermat, Kummer and others, motivating new ideas and techniques by explaining the problems which led to their by:

such extension can be represented as all polynomials in an algebraic number α: K = Q(α) = (Xm n=0 anα n: a n ∈ Q). Here α is a root of a polynomial with coeﬃcients in Q. Algebraic number theory involves using techniques from (mostly commutative) algebra and ﬁnite group theory to gain a deeper understanding of number Size: KB. Book recommendations for people who like Introductory Algebraic Number Theory by Saban Alaca, Kenneth S Williams. Register for free to build your own book lists Books. Number theory is a vast and sprawling subject, and over the years this book has acquired many new chapters. In order to keep the length of this edition to a reasonable size, Chapters 47–50 have been removed from the printed version of the book. These omitted chapters are freely available by clicking the following link: Chapters 47– 2 Preface These notes serve as course notes for an undergraduate course in number the- ory. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be ad- dressed in a course in number theory.

A catalog record for this book is available from the British Library. Library of Congress Cataloging in Publication Data Alaca, Saban, – Introductory algebraic number theory / Saban Alaca, Kenneth S. Williams. p. cm. Includes bibliographical references and index. ISBN (hb.) – ISBN (pbk.) 1. Algebraic number. Introductory Algebraic Number Theory by Saban Alaca () [Saban Alaca;Kenneth S. Williams] on *FREE* shipping on qualifying offers. Will be shipped from US. Used books may not include companion materials, may have some shelf wear, may contain highlighting/notes/5(7). An algebraic number ﬁeld is a ﬁnite extension of Q; an algebraic number is an element of an algebraic number ﬁeld. Algebraic number theory studies the arithmetic of algebraic number ﬁelds — the ring of integers in the number ﬁeld, the ideals and units in the ring of integers, the extent to which unique factorization holds, and so on. This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and by: