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Okninsky J. — Semigroup algebras
Okninsky J. — Semigroup algebras

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Название: Semigroup algebras

Автор: Okninsky J.

Аннотация:

This book is intended as the first attempt to gather and unify the results of the theory of noncommutative semigroup rings. Most of the material comes from the literature of the past 10 years, and several new results are included. We follow the line initiated by Infinite Group Rings by D. S. Passman and his later monograph The Algebraic Structure of Group Rings, and R. Gilmer's Commutative Semigroup Rings. The group ring results are basically the starting point for most of the topics considered, while the case of commutative semigroup rings is a base and a motivation for developing the theory of PI -semigroup-algebras. Since problems on semigroup rings R[S] over an arbitrary ring R often are easily settled once we handle the case where R is a field, or they lead to specific difficult problems on tensor products, only semigroup rings with coefficients in a field (referred to as semigroup algebras) will be considered.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 357

Добавлена в каталог: 05.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\cal J$-class      4
Algebra, algebraic      155 157 161—163
Algebra, Azumaya      313
Algebra, Azumaya, local-global property for      315
Algebra, fir      205
Algebra, Frobenius      197
Algebra, graded      65
Algebra, graded noetherian      77
Algebra, graded, homogeneous component of      65
Algebra, graded, homogeneous subset of      66
Algebra, graded, left noetherian      77
Algebra, graded, radical of      76
Algebra, graded, strongly      77
Algebra, hereditary      206
Algebra, monomial      39 293—311
Algebra, monomial, graph of      305—310
Algebra, Munn      50
Algebra, Munn, basic ideal of      51—56
Algebra, Munn, induced ideal in      52—55
Algebra, Munn, modules over      55—56
Algebra, Munn, radicals of      55—56
Algebra, of matrix type      48
Algebra, PI-      215
Algebra, right T-nilpotent      170
Algebra, semifir      205
Algebra, semihereditarv      206
Algebra, semilocal      155 159
Algebra, separable      313
Algebra, spectrally bounded      155
Algebra, spectrally finite      155
Algebra, spectrally nondegenerated      155
Algebra, structure matrix of      175 197
Ascending chain condition, on principal ideals      145 288—289 330
Ascending chain condition, on right congruences      142 328—329
Ascending chain condition, on right ideas      135 228 302
Baer condition      187
Bass formula      96
Congruence, determined by an ideal      37
Congruence, determined by the radical      161—162 263—264
Congruence, p-separative      69 169 256—259
Congruence, right      3
Congruence, semilattice      67 290
Congruence, separative      69 169 256—259
Convolution      97
Descending chain conditions      159—178
Descending chain conditions, on principal ideals      15—18 27 171 183 192
Dimension, Gelfand-Kirillov      104—105 223 275—285 296 299—300 304—310
Dimension, Krull      275 286—291 329
Dimension, Krull, classical      275—287 300
Gradation      65 297—298
Gradation, nondegenerated      76 130
Graph, chain in      307
Graph, chain in, simple      307
Graph, cycle in      307
Graph, cycle in, simple      307
Graph, doubly cyclic vertex of      309
Graph, Gelfand-Kirillove dimension of      307
Graph, growth function of      306
Graph, Hilbert series of      308
Graph, right multiplication      302
Group algebra, Azumaya      314—318
Group algebra, hereditary      208—209
Group algebra, PI-      216
Group algebra, regular      180
Group algebra, self-injective      188
Group algebra, semifir      207
Group algebra, semihereditary      209
Group algebra, semilocal      163
Group algebra, skew      73 76
Group, abelian-by-fmite      217 227—228 242—243 286
Group, FC-center of      85 108—116 225 267
Group, finite-by-abelian-by-finite      145 224
Group, fundamental      208
Group, large subset of      90
Group, nilpotent      82 96
Group, nilpotent-by-finite      88 95 98 134
Group, of fractions      68 81 120 224 239 268—270 320
Group, of units      3 40 201 207 318—322
Group, polycyclic-by-finite      77 129—138
Group, polycyclic-by-finite, subsemigroups of      129
Group, quasicyclic      170
Group, unique product      122
Growth      95 223 307
Ideal, determined by a congruence      34
Ideal, prime      54 90 92 216 277—283 286—288 294
Idempotent set      3
Idempotent set, leftp-subset of      165 171
Lattice, $\cal J$-class      4
Lattice, of right congruences      4
Lattice, of right ideals      34 51—53
Module      55—56 74—75
Module, agebraically compact      190
Module, graded      74
Monoid, bicyclic      4
Monoid, conical      206
Monoid, elementary commutative      199
Ore, condition      81
Ore, subset      89 110 116
Quadruple      96
Radical, Brown-McCoy      265
Radical, Jacobson      56 216
Radical, Jacobson, graded      74
Radical, Kurosh-Amitsur      37 39
Radical, prime      55 216
Radical, strongly prime      265
Rank, $\cal J$-class      4
Rank, of a matrix      8 24—26 243
Rank, of a sandwich matrix      57 241—245
Rank, of a semigroup      275—291 300 330
Sandwich matrix      6
Sandwich matrix, locally invertible      180
Sandwich matrix, p-equivalent columns of      8 166 171
Sandwich matrix, row p-rank of      245
Sandwich matrix, row p-rank of, strong      245
Semigroup algebra      33
Semigroup algebra, algebraic      157 161—163
Semigroup algebra, artinian      172
Semigroup algebra, augmentation ideal of      35
Semigroup algebra, Azumaya      313—325 332
Semigroup algebra, center of      112—115 318—323
Semigroup algebra, commutative      168 256
Semigroup algebra, contracted      37
Semigroup algebra, fir      206
Semigroup algebra, Frobenius      199—202
Semigroup algebra, hereditary      209
Semigroup algebra, K-separable      324
Semigroup algebra, lattice of ideals of      34
Semigroup algebra, local      169
Semigroup algebra, PI-      213 239 299—304
Semigroup algebra, prime      91 114 294 331
Semigroup algebra, prime PI-      267—273
Semigroup algebra, quasi-Frobenius      196
Semigroup algebra, radical of Jacobson      36 42 121 131—133 160—166 174—177 217 255—266 297—301 329 331
Semigroup algebra, radical of locally nilpotent      132 295
Semigroup algebra, radical of prime      90 133 259—261 286 295
Semigroup algebra, regular      179—186 253 327—328
Semigroup algebra, right chained      170
Semigroup algebra, right fir      207
Semigroup algebra, right noetherian      40 131 135—137 141—151 228 236 302—303 328—329
Semigroup algebra, right perfect      170 193
Semigroup algebra, satisfying a polynomial identity      see “PI-”
Semigroup algebra, self-injective      187 328
Semigroup algebra, semifir      207 333
Semigroup algebra, semihereditary      210—211
Semigroup algebra, semilocal      160—168 248 327
Semigroup algebra, semiprimary      172 248
Semigroup algebra, semiprime      91 294
Semigroup algebra, semisimple artinian      173 176 198
Semigroup algebra, with trivial units      121
Semigroup, $\pi$-regular      21—28 333
Semigroup, $\pi$-regular, strongly      21 249
Semigroup, 0-cancellative      10 263 286
Semigroup, 0-simple      4 29 229
Semigroup, almost idempotent-free      324
Semigroup, almost weakly nilpotent      88
Semigroup, archimedean components of      67 210 289—290
Semigroup, cancellative      79—138 224—228 239 259 278 318—322
Semigroup, cancellative, FC-center of      108 318—321
Semigroup, center of      3
Semigroup, completely 0-simple      4 6—8 48 92 142—144 146 166—174 181—182 229—234 240—248 268—270 322
Semigroup, completely 0-simple, triangularizable      233
Semigroup, completely semisimple      5
Semigroup, graded      65
Semigroup, idempotent-free      121
Semigroup, inverse      5 60 149 183—185 196 233—236 253
Semigroup, K-complete      257
Semigroup, locally finite      13—17 27 158 174 180—184 222 327
Semigroup, medial      265 291
Semigroup, Nakayama matrix of parameters of      196
Semigroup, nil      10 18—19 26 299
Semigroup, of matrix type      6
Semigroup, of matrix type, row of      6
Semigroup, of matrix units      39
Semigroup, of polynomial growth      95 223 308—309 331
Semigroup, ordered      123
Semigroup, p-separative      69 211 256
Semigroup, periodic      5 157 160 171 180 222
Semigroup, permutative      257—259 284—285
Semigroup, principal factor      4
Semigroup, radical of, locally nilpotent      295
Semigroup, radical of, nil      295
Semigroup, radical of, prime      295
Semigroup, Rees factor      4
Semigroup, regular      5 180
Semigroup, rigid      206
Semigroup, semisimple      5 22 249
Semigroup, separative      67 260
Semigroup, skew linear      8—11 19 25—30 142 250 279—280 333
Semigroup, skew linear, irreducible      10 237 269 271
Semigroup, strongly p-semisimple      60 173 185 196 253
Semigroup, T-nilpotent      18 171
Semigroup, torsion-free commutative      91
Semigroup, unique product      119—128 131
Semigroup, weakly nilpotent      83 98 133
Semigroup, weakly periodic      21—31 149 249—251
Semigroup, with permutational property      221—238 276 279 281 289 299—301 332
Semilattice, of groups      210
Semilattice, of semigroups      67 70 260—261 265
Smash product      71—75
Spectrum      155
Subsemigroup, free      81 93 133—134 304
Subsemigroup, left group-like      41—44
Subsemigroup, of finite index      88
Support      34
Theorem, Amitsur-Levitzki      216
Theorem, Braun      216
Theorem, Grigorchuk      96
Theorem, Gromov      95
Theorem, Kaplansky      216
Theorem, Maschke      173 243
Theorem, Osofcky      193
Theorem, Posner      216
Theorem, Shirshov      222
von Neumann regular element      153
Word, periodic      301
Word, primitive      295—301
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