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
a₁ algebraic integer algebraic over F ANALYSIS applications assertion associated assume Bibliography called Chapter Classic common complete congruence conjugates Consider contains Conversely Corollary covers defined denote determinant DIFFERENTIAL discriminant distinct divides divisible divisor edition element elementary equation established example exist expressed extension fact factors field Find follows functions fundamental Gaussian give given Hence ideal illustrations independent integral basis integral coefficients INTRODUCTION irreducible least Lemma linearly MATHEMATICAL maximal mean mechanics method minimal polynomial modulo non-zero norm Note obtain otherwise P₁ PHYSICS polynomial positive possible preceding prime ideals primitive principal problems proof properties prove rational integers rational prime relatively prime residue result root satisfies Show solution STATISTICAL suppose symmetric Theorem theory unique unit write written 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 |