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Karpilovsky G. — Unit groups of classical rings
Karpilovsky G. — Unit groups of classical rings

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Название: Unit groups of classical rings

Автор: Karpilovsky G.

Аннотация:

The subject matter of this book lies at the crossroads of four areas: ring theory, group theory, group representation theory, and algebraic number theory. Like so many interdisciplinary studies, it has its fascinations and attractions, but also its inherent dilemmas. A multitude of concepts and devices pertaining to the structure of groups and rings, algebraic АГ-theory, algebraic and analytic number theory, valuation theory, and group representation theory are used in open or disguised form to investigate the structure of the unit group of a particular ring. This provides for a vivid interplay among, and is a source of enrichment for, the mentioned disciplines. The leitmotif in our discussion is created by the following two related problems.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 370

Добавлена в каталог: 11.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute ramification index      120
Absolute residue degree      120
Algebraic algebra      183
Algebraic element      183
Amitsur      199
Apostol      80
Artin      104 227 228
Artin — Rees lemma      227
Associated primes      93
Augmentation      249
Augmentation ideal      249
Augmentation map      249
Ayoub, C. W.      342
Ayoub, R. G.      342
B-high subgroup      157
Baer      98 99
Bass      88 225 233 234 240 242 243 244
Bass independence theorem      88
Bernstein      45 54
Borel      245
Bounded subset      21
Bourbaki      2 21 155 242 111
Brandis      136 144
Brauer      185
Canonical fundamental unit      50
Carin      161
Cartan      185
CHARACTER      74
Character, Dirichlet      76
Character, identity      74
Character, primitive      76
Character, principal      74
Characteristic      2
Chevalley      16 22
Chevalley — Hasse theorem      22
Class group      3
Class number formula      80
Cliff      292 300 305 306 308
Codifferent      136
Cohen      119
Cohn, J. A.      262
Cohn, J. H. E.      54
Cohn, P. M.      2 168 212
Concalves      201 205 206 207 208 210 310
Conductor      76
Congruence subgroup      225
Content      239
Continuons chain of finite extensions      158
Cube-free integer      45
Curtis      276
Dedekind      15 46 79 231
Dedekind domain      3
Dedekind zeta-function      79
Degert      44
delaunay      45 53 54
Dennis      292
Dirichlet      16 24 76 77 175 233
Dirichlet L-function      78
Dirichlet unit theorem      24
Discriminant      6
Discriminant ideal      4
Division ring      179
Eisenstein      128
Elementary matrix      234
Elementary row operation      238
Elementary subgroup      234
Euler function      7
Exponent of Galois extension      151
F-conjugate      322
F-conjugate, characters      322
F-conjugate, classes      322
F-conjugate, idempotents      323
Faddeev      54
Field      5
Field extension      5
Field extension, abelian      154
Field extension, cyclic      6
Field extension, finitely generated      5
Field extension, Galois      6
Field extension, separable      6
Field extension, solvable      154
Field extension, totally ramified      122
Field extension, unramified      122
Field, complete      8
Field, complete discrete valued      112
Field, completion of      8
Field, finitely generated      5
Field, first kind      46
Field, fixed      5
Field, formally real      106
Field, function      102
Field, global      102
Field, imaginary quadratic      34
Field, local      112
Field, p-adic      127
Field, perfect      116
Field, pure cubic      45
Field, rational p-adic      108
Field, real closed      106
Field, real quadratic      34
Field, second kind      46
Field, totally complex      10
Field, totally real      10
First factor      72
Fomin      99
Formal power series      119
Fractional ideal      3
Franz      87
Franz independence lemma      87
Fuchs      11 107
Fundamental system      25 344
Fundamental unit      25
Gauss      77
Gauss sum      77
Gilmer      217
Gilmer's theorem      217
Goncalves — Mandel’s conjecture      206
Gorenstein      307
Group      1
Group algebra      246
Group of type $p^{\infty}$      95
Group ring      246
Group, binary tetrahedral      11
Group, bounded      2
Group, circle      175
Group, cyclic      1
Group, dicyclic      11
Group, dihedral      286
Group, divisible      2
Group, elementary abelian      96
Group, free modulo torsion      1
Group, full rational      95
Group, hamiltonian      268
Group, linear      203
Group, multiplicative      1
Group, p-component of      1
Group, periodic      182
Group, quasi-cyclic      95
Group, quaternion      11
Group, reduced      2
Group, right-ordered      270
Group, splitting      1
Group, torsion      1
Group, torsion-free      1
Group, unique product      269
Group, weakly nilpotent      188
Hall      268
Harish — Chandra      245
Hartley      315 316
Hasse      16 22 123 124
Height      97
Hensel      131 134
Hensel's lemma      9
Herstein      189 198 199 200 205
Herstein’s conjecture      198
Higman      267 268 321 342
hilbert      349
Hilbert’s basis theorem      3 227
Homological dimension      241
Hua      185
Huppert      301 306
Huzurbazar      186
Idempotent      2
Idempotent, orthogonal      2
Idempotent, primitive      2
Idempotent, subalgebra      337
Idempotent, trivial      2
Independent system      20
Inertia field      124
Infinite general linear group      235
Inner automorphism      274
Integral domain      3
Integral element      3
Involution      280
Irreducible component      242
Irreducible topological space      242
Isometric isomorphism      8
Jacobson      101
Jacobson radical      2
Janusz      2 295
Kaplansky      184 345
Karpilovsky      275 276 327 329 330 339
Kneser      146
Krempa      229 232 273
kronecker      15 30
Krull      231 232 243
Krull dimension      243
Krull domain      231
Kulikov      97
Kummer      83
Lang      2 80 81 174
Latimer      28
legendre      40
Legendre symbol      40
Lichtman      206 210 213
Lichtman's conjecture      206
Livingstone      262
Lueroth      143
Malek      228
Mandel      201 205 206 208 210
Matsumura      244
Maximal divisible subgroup      2
Maximal torsion subgroup      1
May      141 149 153 154 156 158 160 161 165 166 167 168 169 173 175 233 318 326 327 332 333 334 337 339 342
Milnor      82 225 343
Minkowski      30
Monastymyi      205
Monomial      247
Multiplicative residue system      112
Nagao      242
Nagell      45 53 54 55 60
Narkiewicz      5
Nil ideal      2
Nilpotent element      2
Nilpotent ideal      2
Nilradical      2
Noether      208
Noether's normalization theorem      230
Noetherian space      242
Non-quadratic residue      40
Norm      4
Norm homomorphism      5
Normalization      189
Normalized group basis      265
Normalized unit      253
Order      119
Outer automorphism group      274
p-rank      97
Passman      256 258 261 263 288 290
Pearson      217 220
Pell's equation      36
Perlis      324
Pickel      315 316
Place      257
Prime element      93
Prime of field      7
Prime subring      2
Principal fractional ideal      3
Product formula      17
Projective map      251
Projective resolution      241
Pruefer      98
Pure subgroup      99
Quadratic residue      40
Quadratic symbol      174
Quaternion algebra      313
Ramachandra      82
Ramification index      4
Ramified prime      4
Rees      227 228
Regular representation      256
Regulator      26
Reiner      276
Relative class number      72
Residue degree      4
Residue system      112
Richaud      44
Riemann      78
Riemann zeta function      78
Right global dimension      242
Ring      1
Ring of p-adic integers      108
Ring, associative      1
Ring, euclidean      238
Ring, finitely generated      2
Ring, primary      215
Ring, projective limit      108
Ring, reduced      2
Ring, semisimple      2
Ring, torsion-free      11
Roggenkamp      292
Roquette      119 231 232
Rossa      274
S-unit      16
S-unit group      16
Saksonov      260 327
Samuel      232
Schenkman      161
Schneider      217 220
schur      204
Scott, W. R.      189
Sehgal      261 279 300 305 306 308 315
Serre      280
Signature      10
Skolem      208
Skolem — Noether theorem      200
smith      263 288 290
Special Whitehead group      238
Square-free integer      31
Square-free part      31
Stender      45
Strojnowski      271
Stuth      195 196 197
Subnormal subgroup      184
Support      247
Supporting subgroup      247
Supporting subring      247
Tits      207
Torsion subgroup      1
Torsion-free rank      97
1 2
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