Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
O'Donnell C.J. — Incidence Algebras
O'Donnell C.J. — Incidence Algebras

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Incidence Algebras

Автор: O'Donnell C.J.

Аннотация:

While the incidence algebra of a locally finite partially ordered set X over a commutative ring /?, denoted 1{Х, Л), was introduced in the mid 1960's as a natural setting for the study of some combinatorial problems, it soon became apparent, that this algebra was an interesting object to study. In particular, it includes such standard ring theory examples as the product of copies of a ring R and the ring of upper triangular matrices over Л. The papers by Farkas Doubilet, Rota, and Stanlev and Leroux and Sarraille each investigated some algebraic aspects of incidence algebras and each also expressed the hope that their work would stimulate the interest of other researchers. In this direction, many properties of incidence algebras have been obtained, yet no single source indicative of the current level of knowledge on this subject is available. It is the purpose of the second part of this work (Chapters 4 through 8) to present some of the directions of development that have been explored. The book does not


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 355

Добавлена в каталог: 19.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$n \times n$ board      141
$\hat{b}$      226 227
${P}_{u}$ ideal      189—194 197 198 200—202 217—224 227 228 230
${\mathcal U}_{p}$ filter      189 190 218
2-subset      5—8
Algebra, anti-isomorphism      147
Algebra, boolean      3 42 47 49 71 91 110 144 165—167 175 189 190 196 199 202 219 225 226
Algebra, Boolean, complete      272
Algebra, dual      133 150
Algebra, embedding      171 186 187
Algebra, finite-dimensional      171
Algebra, isomorphism      15 16 19 24 27 28 32 53 56 77 111 113—117 119 120 133 136 137 157 170—173 186 187 237 261 263 279 299
Algebra, PI      297 298
Algebra, right regular representation      171
Algebra, subalgehra      19 28 31
Algebra, topological      10 18
Algebraic closure      44 87
Algebraic topology      50
Amitsur Levitski Theorem      299
Annihilator      95 242
Antichain      3 15 30 35 46 199 202 220 224—229 237—239 265 281 294 305
Antichain, maximal      220 225—227 259 294
Antipode      132 151 152 157—161
Antisymmetry      1
Associative law      17 121
atom      47 73—76
Augmentation      121
Bialgebra      130 131 133 136 140 141 143—146 149—152 157 159
Bialgebra, binomial      161
Bialgebra, Dirichlet      157
Bialgebra, Faa di Bruno      148 159
Bialgebra, hereditary      144 161
Block, partition      71—73 90 92 102 103 105 108 144 145 159 100 244 271
Cantor — Bendixson      228—230
Category      137—139
Category, isomorphism      139 140
Category, locally finite      137—139
Category, Moebius      18
Category, subcategory      138 139
Cayley — Hamilton theorem      23 24
Center, group      84
Center, incidence algebra      29—31 262 27
Chain      3
Chain, incomparable      219 221 245
Chain, length      3 5 11 37 38 158 161 174 233 240 245 246 293 300
Chain, maximal      46 73 74 113—115 158
Chain, of filters      166
Chain, of ideals      272
Chain, of ideals, prime      217 240 246—248
Characteristic zero      11 20 21 23 110 113 116 127 192
Chief series      82—84
Closed, element      45 46
Closed, map      198 208 219
Closed, set      195 196 198 202 208 209
Closure operator      44—46 52
Coalgebra      121—133 135—137 141 157
Coalgebra, binomial      132 133
Coalgebra, Boolean      132 141
Coalgebra, cleavage      141
Coalgebra, combinatorial      126
Coalgebra, Dirichlet      136 157
Coalgebra, divided powers      135 156 157
Coalgebra, divided powers, multivariate      135
Coalgebra, dual      135—137 157
Coalgebra, embedding      154
Coalgebra, Eulerian      137 144
Coalgebra, Faa di Bruno      145 146
Coalgebra, finite point lattice      141
Coalgebra, infinitesimal      141
Coalgebra, isomorphism      132 133 157
Coalgebra, Quotient      123
Coalgebra, subcoalgebra      126 127
Coassociative law      121 128
Coatom      47 65 76
Cobounded      174 175 187 189 190 192 193 199 220 222 223 227
Cocommutative      128 137 146
Coefficient, binomial      127 131
Coefficient, bisection      131 132 141
Coefficient, Faa di Bruno      145
Coefficient, Gaussian      68 136 137
Coefficient, incidence      109 111 140
Coefficient, q-binomial      68 116
Coefficient, section      127—129 131 132 136 141 145
Cofinite set      2 230
Coideal      122 124 129 130 138 140
COLOR      101 134
Coloring      101 105 134
Coloring, weight      101 102 104 105
Combinatorics      9 18 33 39 87 122 141 160 161
Compact      195
Compact, Hausdorff      228—230
Compact, Hausdorff, degree      228 229
Compact, Hausdorff, rank      228 229
Compact, regularly      293 296
Complement, of an element      165 167
Complement, set      230 245
Comultiplication      121 128 138 141
Conjugacy class      84 139 140
Connected component      9 15 29 263 264
Containment map      200 203 204 206—209 232 237
Containment set      203 205 214
Convex hull      4 23 24 193 220
Convex set      4 24 174 175 192 193 219 221
Convolution      150 151 153 156 157 159
Coset      103 215
Counitary product law      121 122
Counitmap      121 123 124 128 138 141 149
Countable intersection property      293 296
Cover      3 30 46 47 73—75
Cross cut      46—49 65
CYCLE      91—93 103—105
Cycle, disjoint      91—93 102
Cycle, length      91—93
DCC      306
de Bruijn's Theorem      102 105
Depth      294
Depth, finite      294 296
Derivation      141 251—256 259
Derivation, additive      253—258
Derivation, higher      259
Derivation, inner      252 255 256 259
Derived set      228
Diagonalization      121 123 129 130 149
Differentiation operator      161
Dirichlet, bialgebra      157
Dirichlet, coalgebra      136 157
Dirichlet, convolution      157
Dirichlet, series      28 157
Dirichlet, series, multivariate      136
Dual, algebra      133 150
Dual, coalgebra      135—137 157
Dual, lattice      47 49
Dual, poset      2 39
Dual, space, linear      125
e function      19 21
E-equivalence      19 24
Eificnspace      171
Eigenvalue      171
Enumeration problem      137
Equivalence class      1 4 9 19 20 24 26 101 102 104 105 107 129 129 285 301
Equivalence relation      1 4 9 19 25 26 107—110 112 115 129 133 136 138 148 153 211 285 301
Equivalence relation, compatible (on morphisms)      138
Equivalence relation, order compatible      19 20 23 25 107—109 112 128—130 132 133 136 141—144 148 149 151 152 155
Euler, characteristic      50—52
Euler, characteristic, reduced      50
Euler, phi function      103
Face      50
Field, dimension      50
Field, extension      44 87
Field, extension, degree      87
Field, extension, dimension      87
Field, finite      44 66—69 71 87 93 94 115
Field, order      44 69 87 93 94
Field, splitting      87
Field, subfield      44 87 224
Filter      165
Filter, bounded      199 220 227
Filter, prime      166 167 195 196 206 231—233 235 237
Filter, prime, minimal      166 234 235
Filter, principal      34 166 229
Filter, unbounded      199 220 223 227
Fixed point      202
Fully-nilpotent      210 236
Fully-nilpotent, on a set      173
Function, additive      252
Function, algebraic-tally bounded      189 202 217
Function, charactoisistic diagonal      29
Function, fractional      275
Function, Moebius      1 2 29 58 59 65 84 86 91
Function, multiplicative      278 279
Function, nilpotent      177 238 246
Function, potential      256
Function, unbounded      22
G-equivalence      10
Gib      163 164
Graph      9 18 134
Graph, planar      161
Graph, subgraph      135
Graph, theory      135
Graph, vertex      135
Group      18 82 84—273 275
Group, abelian      82—88
Group, abelian, elemental finite      70
Group, center      84
Group, centralizer      9
Group, cyclic      42 71 88 103
Group, direct product      70 83—85
Group, finite      82 83 139
Group, index      93 103
Group, isomorphism      84—86 156 157 159 273 279
Group, multiplicative      42 87
Group, nilpotent      83
Group, normalizer of a      84
Group, of multiplicative functions      156 157 159
Group, order      42 71 83 84 94 103
Group, permutation      101
Group, quotient      82 85
Group, simple      85
Group, simple, finite      84—86
Group, solvable      82 83
Group, solvable, finite      83
Group, subgroup      42 70 71 82—86 101 103
Group, subgroup, automorphism      273—275
Group, subgroup, commutator      80 82
Group, subgroup, complement      82
Group, subgroup, conjugate      102
Group, subgroup, maximal      82—84
Group, subgroup, normal      82—84
Group, subgroup, normal, minimal      82 83
Group, supplement      84 85
Group, Sylow      70 83
Group, symmetric      91 299
Hadamard product      25 26 32 107 252 274
Hasse diagram      3 5 9 22 164 257
Hasse diagram, vertex      3 9
Hausdorff      196
Height      115 293 294
Height, finite      294 295
Homeomorphism      197 198 208 218 221 224 228 229 231 234 238 247—249
Homology      18
Hopf algebra      132 140 151—153 156 161
Hopf algebra, Faa di Bruno      159 160
Hopf algebra, hereditary      153
Hopf algebra, isomorphism      157
Ideal map, maximal      211—215
Ideal map, prime      211 213 231 232
Ideal map, prime, minimal      238
Ideal, maximal      97 168 169 171 185 180 191 193 194 196—200 202 203 206 208 209 213 218 230 234 240—242 248 249 261
Ideal, maximally disjoint      182 234 241 246 247
Ideal, nil      180 181 184 185 306
Ideal, nilpotent      180—184 234—240 242 243 247—249 301 305
Ideal, of a poset      34
Ideal, of a poset, principal      34
Ideal, prime      179—183 185 189 194 195 200 202—204 206 209 210 217 218 220 222 223 230 237 239—244 246
Ideal, prime, minimal      217—219 223 227 228 230 231 234—236 239 249
Ideal, principal      36 306
Idempotent      86 260 261 263 266 272 280 306
Idempotent, central      263
Idempotent, orthogonal      172 261 266 267 278 280
Idempotent, orthogonally split      270 272
Idempotent, pairwise orthogonal      263
Idempotent, pairwise orthogonal primitive      263
Idempotent, primitive      263
Incidence algebra      10
Incidence algebra, algebraic      304
Incidence algebra, automorphism      35 274 278
Incidence algebra, automorphism, inner      35 273 278 279
Incidence algebra, automorphism, outer      281
Incidence algebra, automorphism, standard      279—281
Incidence algebra, basis      26
Incidence algebra, commutative      110
Incidence algebra, direct product      29 40
Incidence algebra, finite dimensional      173
Incidence algebra, free      148
Incidence algebra, invcrtible element of      23 27 33
Incidence algebra, isomorphism      40 260 261—263 266 268 270—273 281
Incidence algebra, PI      299 300
Incidence algebra, quotient      212
Incidence algebra, reduced      27 32 33 107 109—115 130
Incidence algebra, reduced, full binomial type      112—114 116 121
Incidence algebra, reduced, standard      25 26 28 110 116 117 119 120
Incidence algebra, snbalgebra      18—26 28 29 31 32 107 114 117 121 130 185
Incidence algebra, unit      289 291 292
Incidence bialgebra      141 142 153
Incidence bialgebra, embedding      153
Incidence bialgebra, free      149 157
Incidence bialgebra, reduced      132 141 143 144 151
Incidence bialgebra, reduced, free      156
Incidence bialgebra, reduced, standard      144
Incidence coalgebra      124—128 131 135 140—142 151 161
Incidence coalgebra, category      138 139
Incidence coalgebra, free      148
Incidence coalgebra, quotient      138
Incidence coalgebra, reduced      130 132 133 136 137 138 141 149 151 152 156 157 159
Incidence coalgebra, reduced, Boolean      132
Incidence coalgebra, reduced, free      148
Incidence coalgebra, reduced, inner      138—140
Incidence coalgebra, reduced, standard      130 133 135 136 138 139 144 145 149 151 153 157 159
Incidence coalgebra, reduced, strongly      138 139
Incidence coalgebra, subcoalgebra      122 126 127
Incidence Hopf algebra      153 154 157
Incidence Hopf algebra, free      157
Incidence Hopf algebra, reduced      143 152 156
Incidence Hopf algebra, reduced, free      156
Incidence ring isomorphism      262—264 271
Inclusion-Exclusion Principle      43
Indeterminate      27 113 128 146 147 297
Index of nilpotency      176
Integers, under divisibility      2 27 33 43 71 120 136 157 164
Integers, under usual ordering      1 5 18 26 37 41 42 71 127 135 157 164 288
Integral domain      120 174 187 240 243 249
Interval poset, the      48 52
Isomorphism problem      260 264 266 272 273
Join      73 75 108 163 164
Join of atoms      47 73—75
Join of atoms, irredundant decomposition      73—75
Join, semilattice      54—56
Jordan chain condition      73 74 113
Kernel      77 90 95 96 123 124 130
Kronecker delta      127 128
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте