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Jategaonkar A.V. — Localization in Noetherian Rings
Jategaonkar A.V. — Localization in Noetherian Rings

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Название: Localization in Noetherian Rings

Автор: Jategaonkar A.V.

Аннотация:

This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 323

Добавлена в каталог: 20.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-homogeneous module      269
Affiliated series      121 239
Algebra, finite      16 296
Algebra, Lie      298
Algebra, Weyl      2 7
Annihilator      6
Annihilator, right ideal      6
AR property      81ff 140ff
AR ring      84 140ff 225
AR separated ring      224
Artin radical      131
Artinian quotient module      217
Artinian quotient ring      33 211ff
Assassinator      98
Assassinator prime ideal      98
Associated prime ideal      68
Bimodule      18
Bimodule, affiliated series of      121 239
Bimodule, Noetherian      120ff
Bimodulecellular series of      122
Bimoduleirreducible      2 48
Bimodules, subdirect product of      132
BOND      12 3ff
Bond, degenerate internal      140
Bond, density condition for      176
Bond, girth of      178
Bond, internal      139
Bonded rings      124
Bounded uniform dimension      167 199
cell      122
Cellular series      122
Centrally separated ring      225 263ff
Chain      2 86
Clan      2
Classical      193ff
Classical in comparability condition for      151 156 185 191 193 226 238 243
Classical, clique      193ff
Classical, localization      78 188
Classical, order      35
Classical, primary decomposition      243ff
Classical, semi-local ring      78
Classical, subset of spec R      187
Classically      78 83 188 203ff.
Classically, fully semi-primary ring      244
Classically, localizable semi-prime ideal      78 83 188 203
Classically, primary ideal      244
CLIQUE      136 140ff 171 172 193 227
Closed submodule, lo      39
Cogenerated torsion class      10 67
Common multiple      3
Common multiple property      3
Completely prime ideal      14 162 195 300
Compressible module      45ff 59 270
Condition, density      176 183
Condition, incomparability      151 156 185 191 193 226 238 243
Condition, intersection      190 191 194ff 200
Condition, Ore      3 7
Condition, second layer      187 188 202 219 226 251 285
Condition, strong second layer      220 226 251
Convention      39 59
Cotame simple module      280
Countable set      xii
Critical module      2 70
CYCLE      2 86
Decomposition of injectives      92ff
Dedekind ring      289
Degenerate internal bond      140
Degenerate strongest link      181
Dense submodule      10 39
Density condition      176 183
Derivation      20 299
Deviation      2 33 2 34
Deviation of      233 2 34
Dimain      7
Dimain, Ore      7 37
Dimension, classical Krull      230 238
Dimension, GK      2 38
Dimension, global      134
Dimension, Krull      157 234ff 269ff
Dimension, semi-simple      24 41
Dimension, uniform      42 96
Directed graph      (see Link graph)
Discrete poset      2 33
Enough clans      205
Enough invertibles      2 89
Equivalent, prime ideals      135 (see Clique)
Equivalent, prime rings      124ff
Essential subdirect sum      42 96
Essentially compatible      43
examples of      16ff.
Extension      16
Faithful ideal      306
FBN ring      162 171 199 236
FC-subgroup      306
finite      16
Finite, algebra      16 296
Finite, dimensional module      36
Finite, dimensional ring      36 37
Finite, extension      16
First layer      111 117 252
Fractional right ideal      2 76
Fully, bounded Noetherianring      (see FBN ring)
Fully, classical ring      205 245
Fully, semi-primary ring      241ff 247
Fundmanetal, prime ideals      252 256ff 266
Fundmanetal, series      251 252 270ff
Generalized      17 61 122 212 249
Generalized matrix ring      17 61 122 212 249
Generic regularity      (see Sparsity)
girth      178 183
GK dimension      2 38
Global dimension      134
Goldie ideal      66ff 71
Goldie ring      37
Goldie ring, semi-prime      57
Goldie's Theorem      32 5 7
Graph of a ring      136
Graph, directed      (see Link graph)
Graph, locally finite      171
Group, orbitally sound      306
Group, p-nilpotent      309
Group, polycyclic      305
Group, polycyclic-by-finite      305
Group, ring      305ff
Heart of a ring      133
Hereditary ring      2 75
Hereditary subset of spec R      144
HNP ring      275ff
HNP ring with enough invertibles      289
Ideal, classically localizable semiprime      78 83 188 203ff
Ideal, classically primary      244
Ideal, completely prime      14 162 195 300
Ideal, faithful      306
Ideal, fractional      276
Ideal, Goldie      66ff 71
Ideal, Idempotent      14
Ideal, invertible      85 207 279 287ff.
Ideal, irreducible      242
Ideal, localizable semi-prime      71ff
Ideal, minimal prime      38 155 212ff
Ideal, polycentral      86 141 207
Ideal, polynormal      86 141 206ff
Ideal, primary      241 244
Ideal, prime radical of      69
Ideal, reflexive      210
Ideal, singular      56
Idealizer      29
Idempotent ideal      14
Incomparability condition      151 156 185 191 193 226 238 243
Incomparable prime ideals      105 156
Indecomposable nodule      42
Injective module      15 92 290
Injective module, $n^{th}$ layer of      252ff.
Injective module, bimodule      248
Injective module, decomposition of      92ff
Injective module, first layer of      111 117 252
Injective module, fundamental series of      251 270ff.
Injective module, ideal      242
Injective module, pleasant      284 287
Injective module, ring      2 42
Injective module, stem of      284 290ff.
Injective module, tame      115 151 251ff.
Injective module, unpleasant      284 287
Injective module, wild      115 151 251ff.
Internal bond      139
Intersection condition      190 191 194ff. 200
Intersection condition for      19
interval      2 33
Invertible ideal      85 207 279 287ff.
Jacobson radical      72
Jacobson's conjecture      79 120 246ff. 2 72
Krull dimension      157 234ff. 269ff.
Krull dimension, classical      230 238
Layer      116ff.
Layer, $n^{th}$      252ff.
Layer, first      111 252
Layer, second      (see Second layer)
Levitzki's theorem      62
Lie algebra      298
Link      119 135ff. 139ff. 145 151ff. 157 169 175 183
Link graph      136 140ff. 145 171
Link in comparability condition for      151 156 185 191 193 226 238 243
Link, girth of      183
Link, right      135
Link, second layer      135 154
Link, strongest      181ff. 184
Link, trivial      135 141 206 244
Local ring      72
Local!zability criterion      108 116 228
Localizable semi-prime ideal      71ff.
localization      2 71ff. 187
Localization at      12 88ff.
Localization at torsion class      12 88ff.
Localization atcogenerated      10 67
Localization atdefined      11 39 67
Localization atgenerated      11
Localization, classical      78 188
Localization, Ore      2 88
Localization, Partial      217 229
Localization, right      2 71ff. 187
Locally finite      159 167ff. 171 172 224
Locally finite, link graph      159 167ff. 171 172 224
Locally finite, subset of spec R      171
Main Lemma      151ff. 190 203 239 253
Matrix ring      16
Maximal order      210
Minimal prime ideal      38 155 212ff.
Module, $\alpha$-homogeneous      269
Module, annihilator of      6
Module, Artinian quotient      217
Module, assassinator of      98
Module, compressible      45ff. 59 2 70
Module, cotame simple      2 80
Module, critical      2 70
Module, finite dimensional      36
Module, first layer of      111 117 252
Module, fundamental primes of      252 256ff. 266
Module, fundamental series of      251 252 270
Module, indecomposable      42
Module, Jacobson radical of      72
Module, Krull dimension of      234ff. 269ff.
Module, localization of      8
Module, monoform      163 270
Module, nth layer of      252ff.
Module, P-tame      115
Module, P-torsionfree top of      165
Module, P-wild      115
Module, primary      100 105 183 257
Module, primary decomposition of      68 97 101 104 115 241
Module, p—primary      100 183 25 7
Module, quotient      8
Module, S-primary      105
Module, S-torsion      67
Module, S-torsionfree      67
Module, semi-simple      41
Module, semi-simple dimension of      41
Module, serial      285
Module, socle series of      77 271
Module, tame      115 151 251ff.
Module, torsion      10 39 59 67
Module, torsionfree      10 39 59 67
Module, torsionless      48ff.
Module, totally unfaithful      22 3
Module, uniform      42 104
Module, uniform dimension of      42 96
Module, uniserial      282
Module, wild      115 151 251ff.
Modules, essential subdirect sam of      42 96
Modules, similar      43 118
Modules, sub isomorphic      45
Modules, subdirect sum of      42
Mono form module      16 3 2 70
Multiplicative set      2
Multiplicity      112 118 175ff.
Nil radical      62 212ff.
Nil radical of      62 212ff.
Noetherian bimodule      120ff.
Normal element      84
Normalization      155
Normally separated ring      225
Nth layer      252ff.
Orbitally sound group      306
Order      33
Order in Artinian ring      33 211
Order in semi-simple ring      33 37 5 3
Order in skew field      33
Order, classical      35
Order, maximal      210
Order, right      33
Ore's Theorem      3 7
Ore, condition      3 7
Ore, domain      7 37
Ore, localization      2 88
Ore, set      3 11 146
P-nilpotent group      309
P-perfect extension      88
P-primary module      100 183 257
Partial localization      217 229
Period      285 268 296
Pleasant injective      284 287
Polycentral ideal      86 141 2 07
Polycentral ring      87ff. 226 300ff. 308
Polycyclic group      305
Polycyclic-by-finite group      305
Polynormal ideal      86 141 206ff.
Polynormal ring      87ff. 226 301 308
POSET      233
Primary, decomposition      68 97ff. 101 104 115 241 244
Primary, ideal      241 244
Primary, module      100 105 183 25 7
Primary, ring      241
Primary, submodule      101
Prime ideal      xi
Prime ideal, assassinator      98
Prime ideal, associated      68
Prime ideal, completely      14 162 195 300
Prime ideal, fundamental      252 256ff. 266
Prime ideal, minimal      38 155 212ff.
Prime ideal, second layer condition for      188
Prime ideal, strong second layer condition for      220
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