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Nastasescu C., Oystaeyen F.V. — Dimensions of ring theory
Nastasescu C., Oystaeyen F.V. — Dimensions of ring theory

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Название: Dimensions of ring theory

Авторы: Nastasescu C., Oystaeyen F.V.

Аннотация:

The idea of 'dimension', or more generally 'cardinal invariants' is fundamental in many parts of mathematics. Also in algebra, in casu ring and module theory. Here, however, the non-super-expert finds a bewildering variety of notions of dimension;Kroll dimension , (co)homological dimension, Gabriel dimension, Goldie rank, Gelfand-Kirillov dimension, ... . It is far from easy to sort out what the interrelations and differences between all these notions are, when they are defined, when they are equal, ... . Thus it seemed to me that there was reason for a book on the various ideas of dimension in algebra and their interrelations especially because these notions are so useful both in algebra itself and in its manyfold applications. The present authors were willing to take up this considerable challenge, and have produced precisely the kind of book a non-expert needs to find his way through this, at first sight, rather bewildering maze.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1987

Количество страниц: 376

Добавлена в каталог: 23.05.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-critical      127
$\alpha$-critical composition series      131
$\alpha$-critical, res      143
$\alpha$-simple      135
$\alpha$-simple element of L      135
$\mathcal{F}$ - Artinian      224
$\mathcal{F}$ - Krull dimension      233
$\mathcal{F}$ - Noetherian      224
$\mathcal{F}$-(finitely-)cogenerated      224
$\mathcal{F}$-closed      221
$\mathcal{F}$-closure      221
$\mathcal{F}$-finite length      225
$\mathcal{F}$-finitely generated      224
$\mathcal{F}$-saturated      221
$\mathcal{F}$-saturation      221
$\mathcal{F}$-simple      236
$\mathcal{F}$-torsion free      219
$\mathcal{F}$-torsion submodule      218
$\mathcal{F}-\alpha$-critical submodule      232
$\mathcal{F}-\alpha$-simple      240
Additive topology      217
Affine P.l. algebra      335
Almost commutative ring      328
Annihilator of the module      43
Artin - Rees module      204
Artinian (left)      47
Artinian simple ring      54
atom      26
Baer ring      289
Basis      19 41
Basis element      133
Basis series      133
Boolean lattice      33
Centralizing extension of R      84
Centrally Macaulay      309
Character module      76
Classical Krull dimension      178
Clifford system      98
Closed      217
Cogenerated      235
Cogenerator      75
Compact      26
Compact lattice      26
Compactly generated      26
Complement      24
Complemented lattice      24
complete      3
Completely local (ring)      285
Completely prime ideal      286
Composition sequence      50
Compressible      183
continuous      16
Contramodule      42
Convex      121
Cotertiary      204
Critical      127 143
Critical composition series of L      131
Critical socle      146
Crossed product      90
Cyclic submodule      38
Dense      220
Direct factor      31
Direct factor of a      31
Direct family      12
Direct product      40
Direct summand      46 48
Direct union      12
Directed (subset)      16
Discrete filtration      156
Distributive lattice      33
Divisible      117
Docle of M      52
Dual      3
Dual Goldie dimension      17
Endomorphism (ring)      42
Epimorphisms      39
Equivalent      7
Essential      13 48
Essential extension      13
Exact      40
Exact at $M_{n}$      40
Exhaustive (filtration)      156
External) direct sum      41
Factor module      38
Filtered      156
Filtered ring      156
Finite (meet)      10
Finite filtration      326
Finite gr-length      91
Finite height      186
Finite type      41
Finitely co-generated      34
Finitely generated module      41
Finitely presented      114
Flat      80
Flat dimension      275
Flat resolution      275
Frame      314
Free (left) module      41
Fully left bounded      182
G-system      98
Gabriel $\mathcal{F}$-simple      240
Gabriel dimension      135 143
Gabriel dimension of a      135
Gabriel simple      143
Gabriel simple composition series for L      137
Gang      185
Gelfand - Kirillov dimension      315
Gelfand - Kirillov dimension of a k-algebra A      314
Gelfand - Kirillov transcendence degree      330
Generalized crossed product      98
Generalized Rees ring      108
Generate M over R      41
Generator      67
Generators of      41
Global left injective dimension      267
Goldie dimension      13
Good filtration      326
Gr - Artinian      91
Gr - Noetherian      91
Gr-$\alpha$-critical      152
Gr-$\Delta$-injective      229
Gr-$\mathcal{H}$ - Artinian      227
Gr-$\mathcal{H}$ - Noetherian      227
Gr-$\Sigma$-injective      229
Gr-homomorphism      92
Gr-isomorphic      92
Gr-isomorphism      92
Gr-simple      91
Gr.Kdim M      152
Graded (left) submodule      90
Graded a-critical      152
Graded filter      220
Graded left R-module      90
Graded of type G      88
H-ring      195
Height      185
Hereditary torsion class      218
Hilbert - Samuel polynomial      329
Hollow (lattice)      17
Homogeneous component of r of degree $\sigma$      88
Homogeneous components      90
Homogeneous decomposition      88
Homogeneous elements      88
Homogeneous module      340
Homogeneous of degree $\sigma$      90
Homologically homogeneous      309
Hull      74
I-invariant      237
Ideal      18 38
Idempotent      46
Image of f      39
Increasing      4
Indecomposable      31 48
Induced filtration      156
Infemum      3
Injective dimension      265
Injective envelope      74
Injective resolution      264
integral      297
Internal direct sum      46
interval      4
Invariant      160
Invertible      106
Irreducible      48
Isomorphic      4 39
Isomorphism      39
Isotone      4
Isotypic      51
Isotypic $\omega$-component      51
Jacobson radical of M      56
Jacobson radical of R      56
Join      3
Join-irreducible element      10
Kernel of f      39
Krull co-dimension of L      122
Krull dimension      143
Krull dimension of L      122
Krull dimension, res      143
Lattice      3
Lattice isomorphism      4
Lattice morphism      4
Lattice of finite length      9
Leading ideal      161
Left annihilator      43
Left Artin - Rees property      204
Left bounded      182
Left classical ring      206
Left classical ring of fractions      62
Left coherent (ring)      114
Left global (homological) dimension      254
Left Goldie ring      65
Left hereditary ring      274
Left ideals      38
Left limited      92
Left order      65
Left Ore conditions      62
Left permutable      62
Left R-module      37
Left ring of fractions of R with respect to S      62
Left semiart inian      53
Left weak dimension      278
Left-reversible      62
Left-semi-hereditary      280
Length      50
Linear topology (left)      217
Linearly independent      41
Loewy series      29
Loewy-length      29
Lower bound      3
Lower GK-dimension      314 318
Lower-continuous      16
M has graded Krull dimension      152
M-shifted module      220
M-suspension      220
Maximal      5 44
Meet      3
Meet-irreducible      10
Minimal      5
Minimal injective resolution      264
Modular      4
Module homomorphisms      38
Module of formal power series      260
Monomorphic      173
Monomorphic submodules      174
Monomorphiems      39
Multiplicative system      60
Multiplicatively closed set      60
N-dimension regular local (ring)      286
N-ring      209
NIL      58
Nilideal      58
Nilpotent      58
Nilradical      59
Noetherian (left)      47
Nondivisor of zero      62
Normalizing extension of R      83
Normalizing set      285
Normalizing set of generators      285
Opposite      3
Order of u      261
Ore condition (left) with respect to S      62
Ore extension      157
Outer      106
P has height n      211
Positive graded      92
Primary      204
Prime      58
Prime radical      58
Prime ring      59
Projective      7 69
Projective dimension      253
Projective resolution      252
Pseudo-complement      24
Q-prime ideal      160
Quasi - Frobenius (ring)      116
Quasi-invariant      160
Quotient filtration      156
Quotient module      38
R - Macaulay      309
R - S-bimodule      44
R-balanced      76
R-grade      308
R-linear map      38
R-sequence      308
R-submodule      38
Radical      28
Reduced      10
Reduced rank of M      193
refinement      7
Regular      62
Regular normalizing set      285
Relative Gabriel dimension      230 239
Right annihilator      43
Right global dimension      255
Right hereditary ring      274
Right ideals      38
Right limited      92
Right R-module      37
Rigid      221
Ring with enough prime ideals      181
S-closed      63
S-saturated      63
S-torsion      64
S-torsion free      64
Satisfy condition H      195
Semi-local      209
Semiartinian      30 52
Semiatomic (lattice)      26
Semiprime      60
Semiprime (ring)      115
Semisimple      51 53
Separated (filtration)      156
Short exact sequence      40
Similar      7
SIMPLE      8
Simple module      49
Simple ring      54
Simplectic radical      57
singular      196
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