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| Alaca S., Williams K.S. — Introductory Algebraic Number Theory |
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| Предметный указатель |
Abel, N.H. 4 26
Abelian group 4
Alaca, S. 177 191
Aleksandrov, P.S. 73
Algebraic integer 74
Algebraic number 75
Algebraic number field 109
Algebraic over a field 75
Almost Euclidean domain 46
Almost Euclidean function 46
Arpaia, P.J. 51
Ascending chain condition 55
Ascending chain of ideals 54
Associate 5
Atlerlon, T.W. 87
Bachet's equation 385
Bachet, C. 385 412
Bachman, G. 262
Ball, W.W.R. 411
Barner, K. 53
Barnes, E.S. 34 51
Basis of an ideal 131
Basis of an ideal in a quadratic field 135
Begehr, H.G.W. 298
Behrbohm, H. 34
Bell, E.T. 25 140 193 298
Berg, E. 34
Bhallacharya, P.B. 234
Binary quadratic form 47 331 336
Biquadratic reciprocity 1 25
Bjerknes, V. 411
Bolzano — Weierstrass theorem 305
Borevich, Z.I. 262 343
Bounded set 301
Bourbaki, N. 87
Brauer, A.T. 34 53
Brawley, J.V. 343
Brilihart, J. 253 262
Brill, A. 159 191 193
Brouncker, W. 267 298
Brown, E. 411
Buhler, W.K. 25
Burckhardt, J.J. 298
Campoli, O.A. 47 51
Cancellation law 3
Carlitz, L. 300 343
Cassels, J.W.S. 411
Centrally symmetric set 306
Chatland, H. 35 51
Chinese remainder theorem 213 217
Clark, D.A. 46 51
Class number 299 313
Closed set 301
Cohen, H. 383
Cohn, P.M. 25 72
Common denominator of a fractional ideal 196
Common index divisor 186
Complete set of conjugates 116
Conjugate fields 115
Conjugate ideal 247
Conjugates of a relative to K 116
Conjugates of an element algebraic over a field 90
Content of a polynomial 83
Continued fraction 264 298
Convex body 301
Convex set 301
Cox, D.A. 25 51
Cubic domain 2
Cubic field 110
Cubic reciprocity 1
Cyclotomic field 102 186 343
Davenport, H. 35 51 53 298 411
Decomposition number 239
Dedekind domain 194
Dedekind, R. 84 87 156 176 184 192—194 240 249 257 262
Degree of a over K 89
Degree of an element algebraic over a field 89
Degree of an extension 100
Degree of the extension K(a) over K 100
Diameter 303
Dick, A. 73
Dickson, L.E. 34 53
Diophantus 385 412
Dirichlet, P.G.L. 25 279 298 322 346
Dirichlets unit theorem 346 383
Discriminant 123 141
Discriminant of a cyclotomic field 187
Discriminant of a field 141
Discriminant of a polynomial 126 140
Discriminant of a quadratic field 141
Discriminant of a set of elements 124
Discriminant of an element 124
Discriminant of an ideal 135
Distributive law 22
Divisibility of fractional ideals 207
Divisibility of integral ideals 204
Divisor 3
Dubois, D.W. 52
Dummit, D.S. 72 192
Edgar, H.M. 411
Eisenstein domain 1
Eisenstein integer 1
Eisenstein's irreducibility criterion 92
Eisenstein, G. 1 25 26
Elementary operations 218
Emerson, E. 402
Engstrom, H.T. 192
Equivalence class 5
Equivalence relation 5
Erdoes, P. 34 53
Euclid 368
Euclidean algorithm 29
Euclidean Domain 27 28
Euclidean function 27 28
Euler, L. 267 298
Eulers phi function 186 383
Factor module 66
Factorization domain 59 60
Fermat, P. 53 267 385
Field 1
Field of quotients 3
Field polynomial 117
Finitely generated module 66
Finkelslein, R. 411
Foote, R.M. 72
Fractional ideal 196
Fraleigh, J.B. 3 25
Free Abelian group 219 235
Frei, G. 384
Funakura,T. 177 192
Fundamental system of units 361 383
Fundamental unit 264 278 373 375
Fundamental unit of norm 1 277
Fundamental unit of norm 1 272
Galois extension 122
Gauss, C.F. 1 26 83 140
Gaussian domain 1
Gaussian integer 1
Generator of a field 178
Gerst, I. 253 262
Girard — Fermat theorem 48 52 53
Goodstein, R.L. 140
Gras, M.-N. 192
Greatest common divisor 11 29 64
Greene's theorem 64
Greene, J. 47 52 72
Harper, M 46
Hartley, B. 73
Hawkes,T.O. 73
Heath — Brown, D.R. 48 52
| Heath, T 411
Heilbronn, H.A. 34
Hilbert basis theorem 57
Hilbert, D. 57
Hoffman, P. 53
Hofreiter, N. 34
Howard, F.T. 217
Hua, L.K. 35
Huard, J.G. 189
Hudson, R.H. 192
Hypercube 302
Ideal 8
Ideal class group 299
Independent units 354
Index of  146
Index of a cubic field 186
Index of afield 178
Inertial degree 237
Inessential discriminant divisor 186
Integer of degree k in 160
Integers of a quadratic field 187
Integral basis 141
Integral basis of a cyclotomic field 187
Integral closure 81 87
Integral domain 1
Integral ideal 196 218
Integral over a domain 74
Integrally closed 84
Integrally closed domain 84
Irreducible 6
Jackson, T. 48
Jacobson, N. 73
Jain, S.K. 234
Jodeit, M.A 28 52
Jones, B.W. 402
K-conjugates of a 116
Keston, J.F. 35
Kimberling, C.H. 73
Kinkade, L. 25
Kisilevsky, H. 192
Ko, C. 35
Koch, H. 298
Kramer, J. 298
Kronecker symbol 246
Kummer, E. 193
Lagrange, J.-U. 267
Lattice 300
Lattice points 300
Legendre symbol 48 242 246
Lenstra, H.W. 298
Levesque, C. 383
Limit point 301
Llorente, P 177 186 192
London, H. 411
MacDuffee, C.C. 234
Magnification 301
Mahoney, M.S. 53
Mann, H.B. 192 263
Marcus, D.A. 343
Masley, J.M. 343
Masser, D.W. 140
Maximal condition 56
Maximal ideal 16
Min, S.H. 35
Minimal index of a field 178
Minimal integer 164
Minimal integer of degree k in 163 164
Minimal polynomial of an element algebraic over a field 89
Minkowski bound 311 313 314
Minkowski's Convex Body Theorem 305 306
Minkowski's linear forms theorem 306 307
Minkowski's translate theorem 302
Minkowski, H. 299
Mirsky, L. 140
Module 64
Module homomorphism 67
Module isomorphism 67
Mollin, R.A. 193
Molzkin, Th. 52
Monogenic number field 158 249
Monomorphism 112
Montgomery, H.L. 298 343 383
Mordell, L.J. 402 411 412
Multiple extension 102
Muskat, J.B. 343
Myers, B.T. 411
Nagpaul, S.R. 234
Narkiewicz, W. 187 192
Nart, E. 177 186 192
Neighborhood 301
Niven, L 298
Noelher, E. 54 73
Noetherian domain 54 55 57 58
Noetherian module 67
Noetherian ring 55
Norm of a fractional ideal 231
Norm of a prime ideal 237
Norm of a principal ideal 145
Norm of an element 222
Norm of an ideal 142 218
Norm-Euclidean 30 32
Normal extension 122
Normal field 344
Oppenheim, A. 35
Order of an element with respect to a prime ideal 209
Order of an ideal with respect to a prime ideal 207
Ore, O. 25 26
p-Eisenstein 92
Patz, W. 298
Pell's equation 298
Pell, J. 267 298
Perron, O. 35 53
Power basis 158 178
Prime 5 6
Prime ideal 18
Prime ideal lying over a rational prime 237
Prime lying below a prime ideal 237
Primitive polynomial 83
Principal ideal 9
Principal ideal domain 10 27 29 30 56 60 61
Principal ideal ring 25
Product of ideals 21
Proper ideal 9
Pure cubic field 174
Quadratic domain 2
Quadratic field 110
Quartic field 110
Quotient 27 28
Quotient field 3 111
Ramification 240
Ramification index 239
Redei, L. 35 51
Reducible 6
Reflexive property 3 5
Regulator 380
Reid, C. 73
Remainder 27 28
Remak, R. 35 53
Rhai, T.-S. 28 52
Ring of integers of an algebraic number field 110
Rogers, C.A. 53
Rogers, K. 52
Ross, A.E. 192
Rowe, D.E. 25
Rudin, W. 73
Samuel, P. 46 52 73 217
Schappacher, N. 298
Scheinerman, E.R. 108
Schuster, L. 35
Self-conjugate ideal 249
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