The Theory of Algebraic NumbersAn excellent introduction to the basics of algebraic number theory, this concise, well-written 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. |
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Table des matières
DIVISIBILITY | 1 |
THE GAUSSIAN PRIMW | 14 |
POLYNOMIALS OVER A FIELD | 25 |
ALGEBRAIC NUMBER FIELDS | 44 |
BASES | 59 |
ALGEBRAIC INTEGERS AND INTEGRAL BASES | 74 |
ARITHMETIC IN ALGEBRAIC NUMBER FIELDS | 88 |
THE FUNDAMENTAL THEOREM OF IDEAL THEORY | 102 |
CONSEQUENCES OF THE FUNDAMENTAL THEOREM | 120 |
IDEAL CLASSES AND CLASS NUMBERS | 139 |
THE FERMAT CONJECTURE | 146 |
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Expressions et termes fréquents
algebraic extension algebraic integer algebraic number field algebraic over F Bibliography CALCULUS Chapter class number Classic coefficients complete residue system congruence congruent modulo conjugates contains Corollary defined definition denote difierent divides divisible divisor edition element elementary symmetric functions example exist extension of F factorization of integers Fermat field F figures find finite extension finite number first follows form a basis fundamental theorem Gaussian integers Gaussian primes Hence integral basis integral coeflicients introduction irreducible Lemma Let a1 linearly independent MATHEMATICS maximal ideals minimal polynomial modulo monic nomial non-zero ideal number theory polynomial over F positive integer preceding lemma prime ideals prime in G prime number primitive principal problems proof of Theorem properties quadratic field rational integers rational numbers rational prime relatively prime root of unity satisfies set of numbers Show solution suppose symmetric polynomial Theorem 4.6 TnEonEM totality of integers transcendental unique factorization unit zero
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Informations bibliographiques
| Titre | The Theory of Algebraic Numbers Dover books on mathematics Phoenix Edition Series |
| Auteurs | Harry Pollard, Harold G. Diamond |
| Édition | intégrale |
| Éditeur | Courier Corporation, 1998 |
| ISBN | 0486404544, 9780486404547 |
| Longueur | 162 pages |
| Exporter la citation | BiBTeX EndNote RefMan |