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Theory of Algebraic Numbers 3RD Editionby Harry Pollard
Synopses & ReviewsPublisher Comments:An excellent introduction to the basics of algebraic number theory, this concise, wellwritten volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index. Book News Annotation:A brief introduction for undergraduate students and teachers, presenting detailed proofs and explanations of the elementary components of classical algebraic number theory. Begins with divisibility and Gaussian primes, and proceeds to ideal classes and class numbers and the Fermat conjecture. A slightly revised and totally unexpurgated edition of the 1975 publication by the Mathematical Association of America. Annotation c. by Book News, Inc., Portland, OR (booknews@booknews.com)
Synopsis:Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition. Table of ContentsChapter I. Divisibility
1. Uniqueness of factorization 2. A general problem 3. The Gaussian integers Problems Chapter II. The Gaussian Primes 1. Rational and Gaussian primes 2. Congruences 3. Determination of the Gaussian primes 4. Fermat's theorem for Gaussian primes Problems Chapter III. Polynomials over a field 1. The ring of polynomials 2. The Eisenstein irreducibility criterion 3. Symmetric polynomials Problems Chapter IV. Algebraic Number Fields 1. Numbers algebraic over a field 2. Extensions of a field 3. Algebraic and transcendental numbers Problems Chapter V. Bases 1. Bases and finite extensions 2. Properties of finite extensions 3. Conjugates and discriminants 4. The cyclotomic field Problems Chapter VI. Algebraic Integers and Integral Bases 1. Algebraic integers 2. The integers in a quadratic field 3. Integral bases 4. Examples of integral bases Problems Chapter VII. Arithmetic in Algebraic Number Fields 1. Units and primes 2. Units in a quadratic field 3. The uniqueness of factorization 4. Ideals in an algebraic number field Problems Chapter VIII. The Fundamental Theorem of Ideal Theory 1. Basic properties of ideals 2. The classical proof of the unique factorization theorem 3. The modern proof Problems Chapter IX. Consequences of the Fundamental Theorem 1. The highest common factor of two ideals 2. Unique factorization of integers 3. The problem of ramification 4. Congruences and norms 5. Further properties of norms Problems Chapter X. Ideal Classes and Class Numbers 1. Ideal classes 2. Class numbers Problems Chapter XI. The Fermat Conjecture 1. Pythagorean triples 2. The Fermat conjecture 3. Units in cyclotomic fields 4. Kummer's theorem Problems References; List of symbols; Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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