Pollard H., Diamond H.G. — The Theory of Algebraic Numbers :: Электронная библиотека попечительского совета мехмата МГУ

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Pollard H., Diamond H.G. — The Theory of Algebraic Numbers

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Название: The Theory of Algebraic Numbers

Авторы: Pollard H., Diamond H.G.

Аннотация:

An 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.

Язык:

Рубрика: Математика/Теория чисел/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1975

Количество страниц: 162

Добавлена в каталог: 02.12.2004

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Предметный указатель

Algebraic extension of field      46 47
Algebraic integer      74
Algebraic integer number      44 51
Associate      19 88
Baker, A.      56
Basis      59
Basis of ideal      95
Basis, integral      79
Basis, minimal      82
Borevich, Z. I.      149
Class number      139
Complete residue system      16 133
Congruence of Gaussian integers      21
Congruence of Gaussian integers of numbers      15
Congruence of Gaussian integers, modulo an ideal      128
Conjugate of algebraic number      45
Conjugate of algebraic number for a field      65
Conjugate of algebraic number, complex      7
Cummutative ring      25
Cyclotomic polynomial      34
Dedekind — Hasse criterion      124
Degree of algebraic number      45
Degree of algebraic number, of extension      60
Degree of algebraic number, of polynomial      26
Discriminant of basis      67
Discriminant of basis, of field      82
Divide      3 6 26 88 103
Divisor of ideal      103
Eisenstein’s irreducibility criterion      30 33
Elementary symmetric function      36
Equivalence relation      57
Equivalent ideals      139
Euclid      14
Euclidean algorithm      12
Extension of field      46
Extension of field, finite      60 62
Extension of field, multiple algebraic      47
Extension of field, simple algebraic      46
Factor      1
Factorization, uniqueness of      93
Fermat theorem      16 21 134
Fermat Theorem, conjecture ("Last Theorem")      146
Field polynomial      65
Field, algebraic number      44 64
Field, cyclotomic      68
Field, Euclidean      125
Field, finite      42
Field, imaginary      91
Field, non-real      91
Field, number      25
Field, quadratic      77
Fractional ideal      114
Fundamental theorem of algebra      27
Fundamental Theorem of Arithmetic      1 5
Fundamental theorem of ideal theory      102 112 116
Gauss, C. F.      125
Gauss, Lemma      31
Gaussian integer      6
Gaussian integer, prime      14
Gaussian integer, prime classification      18
Gelfond — Schneider theorem      55
Generator of an ideal      97
Greatest common divisor of numbers      16
Greatest common divisor of polynomials      41
Group      25
Hardy, G.H.      11 55 125
Hecke, E.      93
Heilbronn, H.      125
Highest common factor of two ideals      120
Hille, E.      55
Hurwitz, A.      85
Ideal      95
Ideal class      139
Ideal in F[x]      56
Ideal, irreducible      105
Ideal, maximal      105
Ideal, prime      105 116
Ideal, principal      97
Ideal, ramified      126
Ideals, equivalent      139

Infinitude of primes      14 90
Integer in quadratic field      79
Integer, algebraic      74
Integer, Gaussian      6
Integer, rational      6
Integral basis      79
Irreducible ideal      105
Irreducible ideal, polynomial      27
Krull, W.      85
Kummer, E.      149
Kummer, Theorem      155
Landau, E.      55 77 149
Lang, S.      56
Least common multiple of two ideals      136
LeVeque, W. J.      53
Lexicographic order      37
Linear independence      59
Linfoot, E.      125
Liouville, J.      53
Maximal ideal      105
Minimal polynomial      44
Minkowski, H.      140
Monic polynomial      30
Noether, E.      85
Norm of ideal      129
Norm of ideal, of algebraic integer      89
Norm of ideal, of Gaussian integer      7
Number field      25
Ore, O.      112
Polynomial      26
Polynomial, cyclotomic      34
Polynomial, field      65
Polynomial, irreducible      27
Polynomial, minimal      44
Polynomial, monic      30
Polynomial, prime      27
Polynomial, primitive      30
Polynomial, symmetric      35
Prime ideal      105 116
Prime ideal, number      1 6 14 88
Prime, regular      149
Prime, relatively      see “Relatively prime”
Primitive number triple      146
Primitive number triple, polynomial      30
Primitive number triple, root of unity      69
Principal ideal      97
Product of ideals      103
Pythagorean triple      146
Quadratic field      77
Ramified ideal      126
Rational integer      6
Rational integer, root theorem      41
Regular prime      149
Relatively prime ideals      120
Relatively prime ideals, Gaussian integers      21
Relatively prime ideals, polynomials      28
Relatively prime ideals, rational integers      2
Residue class      128
Residue system      16
Ring      25
Root of polynomial      27
Root of polynomial, of unity      69
Roth, K. F.      53
Shafarevich, I. R.      149
Stark, H. M.      125
Symmetric polynomial      35
Symmetric polynomial, homogeneous      36
Thomas, J. M.      50
Trace      126
Transcendental number      51
Unique factorization of ideals      105 112
Unique factorization of integers      1 5 10 123
UNIT      5 6 28 88
Unit in quadratic field      90
Unramified ideal      126
Uspensky, J. V.      68
Vandermonde determinant      68
Vandiver, H. S.      149
Wilson’s Theorem      17
Wright, E. M.      11 55 125
Zero of a polynomial      27

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