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Название: The Elements of the Theory of Algebraic Numbers

Автор: Reid L.W.

Язык: Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1910

Количество страниц: 454

Добавлена в каталог: 15.04.2006

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 0-function, expression for power of prime ideal      359 0-function, for ideals, definition      358 0-function, general expression      38 44 53 359-362 366 367 0-function, in k( )      185-188 0-function, in R, definition      37 0-function, of higher order      54 367 0-function, product theorem      45 360 361 0-function, summation theorem      46 75 362 363 367 Ambiguous ideal      347 Appertains, exponent to which an integer      99 393 Associated integers, in k( )      163 Associated integers, in k( )      223 Associated integers, in k( )      246 Associated integers, in R      9; Basis of conjugate ideals      301 Basis of ideals      293-295 Basis, of ideal      293-295 Basis, of ideal, determination      351-355 Basis, of k( )      159-161 Basis, of k( ))      220 Basis, of k( )      232 Basis, of k( )      245 Basis, of k( )      284-287 Basis, of k( ), determination      289—292 Binomial congruences      110-112 Biquadratic residues and reciprocity law      205-217 Canonical basis of ideals      294 Character of an integer, biquadratic      209 212 Character of an integer, quadratic, in k( )      212 Character of an integer, quadratic, in R      121 Class number of a realm is finite      437 Class number of a realm, definition      434 Class number of a realm, determination      437-448 451 Classes, ideal, definition      432 Classification of the numbers of an ideal with respect to another ideal      326-330 Common divisor of ideals      303 Congruences in k( )      180 Congruences of condition      59-61 190 369-372 Congruences of first degree in one unknown      68-70 Congruences of nth degree in one unknown, preliminary discussion      66-68 374 375 Congruences of second degree with one unknown      119-121 Congruences of two polynomials      57 370 Congruences, 114-116 Congruences, -1 90 387 388 Congruences, common roots      92 93 389 Congruences, composite modulus      95-97 391 392 Congruences, definition      31 297 323 Congruences, determination      93 94 386 Congruences, elementary theorems      32-37 323-326 Congruences, equivalent systems      64; Congruences, Euler’s criterion      115 Congruences, limit to number of roots      89 386 Congruences, multiple roots, definition      89 386 Congruences, primitive and imprimitive roots      111 Congruences, root      66 374 Congruences, solution of \$x^{1}\equiv -1, mod p, by means of Wilson’s theorem      129 130 Congruences, transformations      62-64 372 374 Congruences, with prime modulus      88-90 385-387 Conjugate ideals      301 Conjugate, numbers      4 Conjugate, realm      4 Dirichlet’s theorem regarding infinity of primes in an arithmetical progression      11 Discriminant, of k( )      161 Discriminant, of k( )      221 Discriminant, of k( )      245 Discriminant, of k( )      232 Discriminant, of k( )      287 288 Discriminant, of number      284 Divisibility of ideals      263 303 Divisor, greatest common, discussion of definition      252 Divisor, greatest common, in k( )      173 Divisor, greatest common, in R      16 18 25 Divisor, greatest common, of two ideals      310-313 318 Divisors, of integers in R, number of      23 Divisors, of integers in R, sum of      24; Divisors, of of ideal, number of      318 Equality of ideals      258 259 302 Equivalence of ideals      427-431 Equivalence of ideals in narrower sense      431 Equivalent congruences      62-64 372 373 Eratosthenes, sieve of      10 Euler's criterion for solvability of 115 122 Factorization of a rational prime determined by (d/p), in k( )      179 Factorization of a rational prime determined by (d/p), in k( )      229 Factorization of a rational prime determined by (d/p), in k( )      347 348 Fermat’s theorem      57 Fermat’s theorem as generalized by Euler      57 Fermat’s theorem, analogue for ideals      368 369 Fermat’s theorem, analogue for k( )      189 Frequency of the rational primes      11 Galois realm      281 Gauss’ Lemma      130 General algebraic integers      1 275-279 Generation of realm      3 Ideal numbers, nature explained      254-257 Ideal numbers, necessity for      253 Ideals, definition      257 293 Ideals, determination of basis      298—301 Ideals, introduction of numbers into and omission from symbol      258 295 296 Ideals, numbers defining      295 Ideals, principal and non-principal      260 261 297 Imprimitive numbers      see primitive numbers Incongruent numbers, complete system of, in k( )      182-185 Incongruent numbers, complete system of, in k( )      326 Incongruent numbers, complete system of, in R      34 Index, of a power      106 399 Index, of a product      106 399 Indices, definition      105 399 Indices, solution of congruences by means of      108—110 400-402 Indices, system of      106 399 Integers, absolute value in R      7 33 Integers, of k( )      157 Integers, of k( )      219 Integers, of k( )      245 Integers, of k( )      231 Integers, of k( )      284-287 Integers, of R      7 23 Legendre’s symbol      127 Multiple, least common, in R      25 Multiple, least common, of two ideals      310-312 318 Multiplication of ideals      261 262 302 303 Non-equivalent ideals, complete system of      434 Norm of ideals      326-338 351 Norm, of a number, determination      351 Norm, of a number, in k( )      156 Norm, of a number, in k( )      218 221 Norm, of a number, in k( )      245 Norm, of a number, in k( )      231 Norm, of a number, in k( )      283 Norm, of a number, of an ideal, definition      326 337 Norm, of a number, value      330 Norm, of a prime ideal      338 Norm, of a principal ideal      337 Norm, of a product of ideals      334 Number class, ideal modulus      324 Number class, rational modulus      32 33 Numbers of ideals      293 Numbers, algebraic, conjugate      4 Numbers, algebraic, definition      1 Numbers, algebraic, degree of      1 Numbers, algebraic, of k( )      155 Numbers, algebraic, of k( )      1 218 Numbers, algebraic, of k( )      245 Numbers, algebraic, of k( )      231 Numbers, algebraic, of k( )      281 Numbers, algebraic, of R      7 Numbers, algebraic, of the general realm      271-279 Numbers, algebraic, rational equation of lowest degree satisfied by      2 273 Pell’s equation      423-426 Polynomials in a single variable      268-271 Polynomials with respect to a prime modulus, reduced      62 Polynomials, associated      77 381 Polynomials, common divisor of      76 380 Polynomials, common multiple of      76 380 Polynomials, congruence with respect to a double modulus      81 Polynomials, degree of      76 Polynomials, determination of prime      78 381 382 Polynomials, divisibility of      76 380 Polynomials, division of one by another      382 Polynomials, primary      78 381 Polynomials, prime      78 381 Polynomials, unique factorization theorem for      82-87 382-385 Polynomials, unit      77 381 Power of a prime by which is divisible      26 Primary integers of k( )      193-196 Prime factors, resolution of an ideal into      348-350 Prime ideals      263-265 304 Prime ideals, determination and classification      339-348 Prime ideals, of k( )      263-265 Prime ideals, of k( ), definition      304 Prime numbers, infinite in number      10 Prime numbers, of k( ), classification      177 Prime numbers, of k( ), definition      165 Prime numbers, of k( ), classification      227-230 Prime numbers, of k( ), definition      223 Prime numbers, of k( )      246 247 Prime numbers, of k( ), classification      238-240 Prime numbers, of k( ), definition      235 Prime numbers, of R, definition      9 Primitive numbers, of k( )      157 Primitive numbers, of k( )      218 Primitive numbers, of k( )      282 283 Primitive numbers, of the general realm      274 275; Primitive numbers, with respect to a prime ideal modulus      398 Primitive root, definition      100 Primitive root, determination      112 Primitive root, of prime of form 151 Primitive root, of prime of form is 2      152 Principal class      432 Product of classes      432 Realm, conjugate      4 Realm, definition      3 Realm, degree      4 Realm, generation      3 Realm, number defining      4 280 Realm, number generating      4 Reciprocal classes      434 Reciprocity law, determination of value of (a/p) by means of      144 Reciprocity law, for biquadratic residues      210 215-217 Reciprocity law, for quadratic residues, in k( )      201-205 Reciprocity law, for quadratic residues, in R      135 Reciprocity law, other applications of      149 Residue system, complete, in k( )      182-185 Residue system, complete, in R      33 34 Residue system, complete,in k( )      326 Residue system, reduced, in k( )      185 Residue system, reduced, in k( )      358 Residue system, reduced, in R      37 Residue, odd prime moduli of which an integer is a quadratic      128 145 147 Residue, prime moduli of which 2 is a quadratic      133 Residue, prime moduli of which — 1, is a quadratic      128 Residues of powers, complete system of      98 393 Residues of powers, definition      98 392 Residues of powers, law of periodicity      100 Residues, biquadratic      205-217 Residues, cubic      250 Residues, determination of quadratic      124 Residues, n-ic      116 Residues, quadratic non-      121 Residues, quadratic, in k( )      196-201 Residues, quadratic, in R      121 Residues, with respect to a series of moduli, integer having certain      70 Rummer’s ideal numbers      267 Sub-realm      157 Symbol of ideals      257 295 Symbol, Legendre’s      127 Symbol, Legendre’s for ideal      257 295 Unique factorization theorem, for ideals in k( )      305-317 Unique factorization theorem, graphical discussion of      169 Unique factorization theorem, in k( )      167 174 Unique factorization theorem, in k( )      226 Unique factorization theorem, in k( ), failure of      247-253 Unique factorization theorem, in k( )      236 237; Unique factorization theorem, in R      12 Unique factorization theorem, necessity for      253 Unique factorization theorem, realms in which original method of proof holds      248-250 Unique factorization theorem, restoration in terms of ideal factors      265 266 Unit ideal, of k( )      304 Unit ideal, of k( )      263 Unit, fundamental, determination      420-426 Unit, fundamental, of k( )      233 Unit, fundamental, of k( ), definition      420 Units, of k( )      163 Units, of k( )      222 Units, of k( )      246 Units, of k( )      232-235 Units, of k( ), definition      403 Units, of R      8 Units, realm imaginary      404 Units, realm real      405-426 Wilson’s Theorem      91 Wilson’s theorem analogue for ideals      388 389 Wilson’s theorem as generalized by Gauss      91 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019 | | О проекте