Stenstrom B. — Rings of quotients: an introduction to methods of ring theory :: Электронная библиотека попечительского совета мехмата МГУ

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Stenstrom B. — Rings of quotients: an introduction to methods of ring theory

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Название: Rings of quotients: an introduction to methods of ring theory

Автор: Stenstrom B.

Аннотация:

The theory of rings of quotients has its origin in the work of ф. Ore and K. Asano on the construction of the total ring of fractions, in the 1930*s and 40*s. But the subject did not really develop until the end of the 1950's, when a number of important papers appeared (by R.E. Johnson, Y. Utumi, A. W. Goldie, P. Gabriel, J. Lambek, and others). Since then the progress has been rapid, and the subject has by now attained a stage of maturity, where it is possible to make a systematic account of it (which is the purpose of this book). The most immediate example of a ring of quotients is the field of fractions Q of a commutative integral domain A.

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Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 309

Добавлена в каталог: 02.04.2011

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Предметный указатель

Morita stable      109
Morphism      14 63
Nakayama lemma      179
Natural equivalence      15
Natural isomorphism      127
Natural transformation      15
Nil ideal      182
Nilpotent element      40
Nilpotent ideal      54
Nilpotent, T      183
Noelherian ring      12
Noetherian lattice      67
Noetherian module      12
Noetherian object      123
Noetherian, $\mathcal{P}-$       266
Noetherian, $\mathfrak{F}-$       263
Non-singular module      148
Opposite category      14
Opposite lattice      63
Opposite ring      7
Order      54 62
Order morphism      63
Ore domain      52
Perfect localization      229
Perfect ring      189
Perfect topology      231
Perfectly complete ring      235
Popescu — Gabriel theorem      220
Preadditive category      15
Preradical      136
Preregular set      287
Presheaf      97
Pretorsion      137
Primary decomposition      163
Primary submodule      163
Prime ideal      160
Prime radical      283
Prime ring      54
Primitive idempotent      186
Principal domain      22
PRODUCT      8 85
Product category      16
Projection      8 85
Projective coordinates      20
Projective cover      120
Projective dimension      282
Projective intervals      65
Projective limit      99
Projective module      19
Projective object      89
Prufer domain      61
Pseudo-complement      74
Pseudo-complemented category      117
Pseudo-complemented lattice      74
Pullback      89
Pure      36 212
Pushout      92
Quasi — Frobenius ring      276
Quasi-injective module      158
Quorite ring      285
Quotien module      5
Quotien object      84
Quotient category      199
Radical      136
Radical, Jacobson      179
Radical, prime      283
Rank      127 213 97 177
Rational completion      205
Reduced module      141 159
Reduced ring      40
Reflective ring      284
Reflective subcategory      213
Regular      283
Regular ring      39
Regular ring, complete      78
Regular ring, continuous      252
Regular sequence      174
Regular, M      172
Regularity condition      289
Representable functor      97
Reversible set      52
Ring of finite rank      54
Ring of fractions      50
Ring of fractions, total      52
Ring of quotients      53 196
Ring of quotients, classical      52
Ring of quotients, complete      200
Ring of quotients, flat epimorphic      229
Ring of quotients, maximal      200 196 229
Ring, $\alpha$ -quorite      285
Ring, $\alpha$ -reilective      284
Ring, arithmetical      71
Ring, Artinian      13
Ring, Baer      78
Ring, boolean      41
Ring, classical      170
Ring, Cohen-Macaulay      177
Ring, dominant      226
Ring, fully bounded      165
Ring, group      10
Ring, hereditary      22
Ring, Kasch      235
Ring, local      125
Ring, Noetherian      12
Ring, perfect      189
Ring, perfectly complete      235
Ring, prime      54
Ring, quasi — Frobenius      276
Ring, reduced      40
Ring, regular      39
Ring, self-injective      244
Ring, semi-artinian      183
Ring, semi-hereditary      22

Ring, semi-local      182
Ring, semi-perfect      187
Ring, semi-primary      180
Ring, semi-prime      54
Ring, semi-simple      24
Ring, simple      25
Ring, skew polynomial      53
Ring, strongly regular      40
Ring, Utumi      252
Saturated submodule      62 77 207 283
Schreier refinement theorem      66
Schur’s lemma      24
Sell-injective ring      244
Semi-arlinian module      182
Semi-arlinian ring      183
Semi-hereditary ring      22
Semi-lattice      80
Semi-local ring      182
Semi-perfect ring      187
Semi-primary ring      180
Semi-prime ideal      283
Semi-prime ring      54
Semi-simple module      23
Semi-simple object      128
Semi-simple ring      24
Sheaf      215
Similar intervals      65
Simple module      13
Simple object      128
Simple ring      25
Simple torsion theory      179
singular      55 148
Small category      14
Small subobject      120
Small’s theorem      289
Socle      25 185
Spectral category      128
Spectral category of a category      130
Spectral category of a ring      133
Spectral category, continuous      129
Spectral category, discrete      129
Split exact sequence      8 88
Splitting torsion theory      140
Stable      152 169
Standard representation      223
Stronger topology      147
Strongly regular ring      42
Subcategory      15
Subcategory, abelian      89
Subcategory, full      15
Subcategory, Giraud      214
Subcategory, reflective      213
Sublattice      64
Sublattice, complete      64
Submodule      5
Submodule, $\mathfrak{F}$ -pretorsion      145
Submodule, $\mathfrak{F}$ -saturated      207
Submodule, divisorial      267
Submodule, essential      76
Submodule, primary      163
Submodule, saturated      62 77 283
Submodule, singular      148
Submodule, small      120
Submodule, tertiary      161
Submodule, torsion      57 140
Subobject      83
Subobject, essential      117
Subobject, small      120
Subobject, torsion      140
SUM      88
Supplement      120
Support      172
T-nilpotent      183
Tensor product      26
Tertiary decomposition      162
Tertiary submodule      161
Topological group      143
Topological module      144
Topological ring      144
Topological, linearly      144
topology      145
Topology, $\alpha$ -adic      146 169
Topology, $\mathfrak{F}-$       145
Topology, bounded      150
Topology, canonical      205
Topology, Gabriel      146
Topology, Goldie      148
Topology, l      148 237
Topology, perfect      231
Topology, separated      146
Torsion class      139
Torsion module      57 146
Torsion object      139
Torsion subobject      140
Torsion theory      139
Torsion theory, Goldie      148
Torsion theory, simple      179
Torsion theory, splitting      140
Torsion theory, stable      152
Torsion-free class      139
Torsion-free module      57
Torsion-free object      139
Torsionless module      94
Total ring of fractions      52
Trace ideal      108 113
Trivial extension      45
TTF-class      153
Upper bound      63
Upper continuous lattice      72
Utumi ring      151
Vector space      10
Weaker topology      147
Yoneda Lemma      96
Zero object      83

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