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

$\Sigma$ -generated object      134
$\Sigma$ -injective module      264
AB 5 condition      114
Abelian category      87
Abelian subcategory      89
Additive functor      15
Adjoint functor      103
Algebra      44
Annihilator      13 52
Arithmetical ring      71
Artin — Rees module      169
Artinian lattice      67
Artinian module      13
Artinian object      123
Artinian ring      13
Ascending chain condition      12 67
Associated prime ideal      128 160
Associated prime ideal, weakly      268
atom      73
Automorphism      7
Automorphism category      111
Baer ring      78
Basis for a module      9
Basis for a topology      145
Bezout Domain      53
Bicommutator      7
Bimodule      7 31
Bimorphism      233
Boolean algebra      70
Boolean ring      41
Boolean subalgebra      71
Bounded topology      150
Brouwer lattice      76
Canonical topology      205
Category      14
Category dual      14
Category, abelian      87
Category, automorphism      111
Category, cocomplete      99
Category, complete      99
Category, diagram      97
Category, endomorphism      111
Category, functor      95
Category, Grothendieck      114
Category, locally coirreducible      133
Category, locally finitely generated      122
Category, locally noetherian      123
Category, locally small      94
Category, preadditive      15
Category, quotient      199
Category, small      14
Category, spectral      128
Central idempotent      40
Centrally splitting      140 154
Classical noetherian ring      170
Classical ring of quotients      52
Closed module      198
Closure operator      76
Closure operator, finitary      77
Closure system      65
Cocomplete category      100
Codivisorial module      267
Cogenerate a module      94
Cogenerate a torsion theory      139
Cogenerator      93
Cohen — Macaulay ring      177
Coherent module      42
Coherent ring      43
Coirreducible      119
Cokernel      84
Colimit      99
Compact      73
Compactly generated lattice      73
Compatible      98
Complement      65
Complemented lattice      65
Complete category      99
Complete lattice      64
Complete regular ring      78
Complete ring of quotients      200
Complete sublattice      64
Completion      64
Completion of boolean algebra      79
Completion, Dedekind — MacNeille      65 79
Completion, ideal      80
Completion, rational      204
Composition chain      67
Composition factor      183
Continuous lattice      72
Continuous regular ring      252
Continuous spectral category      129
Coproduct      85
Copure sequence      212
Cotertiary module      161
Countercyclic module      206
Countermodule      206
Critical ideal      212
Dedekind — MacNeille completion      65 79
Dedeking domain      61
Denominator set      52
Dense      149
Depth      174
Descending chain condition      54 67
Diagram category      97
Direct family of subobjects      102
Direct limit      17
Direct product      8
Direct sum      8 85 88
Direct summand      10
Direct system      17 98
Direct union      19 114
Directed set      17
Discrete spectral category      129
Distributive lattice      69
Divisible module      22 58 141 155
Divisorial submodule      267 269
Dominant dimension      211
Dominant ring      226
Dominated element      225
Dominion      225
Endomorphism      7
Endomorphism category      111
Endomorphism ring      7
Envelope, $\mathfrak{F}$ -injective      201
Envelope, injective      118
Epimorphism      6 45 83
Epimorphism of rings      225
EQUIVALENCE      82
Equivalent idempotents      193
Equivalent monomorphisms      83
Essential      54 75 76 117
Essential extension      75
Essentially closed      75
Exact functor      16 89
Exact sequence      6 88
Faithful functor      15
Faithful module      44
Faithfully flat      48
Filter      64
Finitary closure operator      77
Finite length      67 68 92
Finite localization      239
Finite rank      54 126
Finitely generated      10 121
Finitely presented      11 122
Flat epimorphic ring of quotients      229
Flat module      33
Flat module, $\mathfrak{F}-$       212
Flat, faithfully      48
Free module      9

Free on a set      10
Frobenius algebra      278
Fully bounded ring      165
functor      14
Functor category      95
Functor, additive      15
Functor, adjoint      103
Functor, contravariant      15
Functor, exact      16 89
Functor, faithful      15
Functor, full      15
Functor, Horn      16
Functor, left exact      16 89
Functor, representable      97
Gabriel topology      146
Gabriel — Oberst theorem      245
Galois connection      77
Generate a module      94
Generate a torsion theory      139
Generators of a category      93 94
Generators of a module      9
Giraud subcategory      214
Goldie theorem      54
Goldie topology      148
Grothendieck category      114
Height      175
Hereditary class      138
Hereditary ring      22
Hereditary torsion theory      141
Hilbert basis theorem      12
Homomorphism of boolean algebras      71
Homomorphism of modules      5
Ideal      64 80
Ideal completion      80
Ideal, principal      64
Idempotent      10
Idempotent lifting      186
Idempotent preradical      136
Idempotent, primitive      186
Image      6 88
Imbedding      97
Indecomposable      10 119
Independent family      88
Independent, linearly      9
Inductive limit      99
Injection      8 85
Injective cogenerator      21
Injective envelope      118 201
Injective module      20
Injective object      89
Injective, $\mathfrak{F}-$       198
Injective, $\Sigma-$       264
Injective, S      58
Intersection      88
interval      64
Inverse limit      99
Inverse system      98
Invertible ideal      59
Invertible module      209
Irreducible decomposition      69
Irreducible element      69
Irreducible subobject      119
Irredundant decomposition      69
Isomorphism      6 14 82
Isomorphism, natural      27
Isotypic module      164
Jacobson radical      179
Join      63 64
Jordan — Holder theorem      67 68 92
Kasch ring      235
Kernel      6 84
Krull dimension      175
Krull domain      269
Krull intersection theorem      171
Krull — Remak — Schmidt — Azumaya theorem      126
Lattice      63
Lattice anti-morphism      64
Lattice morphism      63
Lattice of finite length      67
Lattice, big      89
Lattice, Brouwer      76
Lattice, compactly generated      73
Lattice, complemented      65
Lattice, complete      64
Lattice, continuous      72
Lattice, distributive      69
Lattice, locally atomic      73
Lattice, modular      65
Lattice, opposite      63
Lattice, upper continuous      72
Length      67
LIMIT      99
Limit, direct      17
Limit, inductive      99
Limit, inverse      99
Limit, projective      99
Linearly topological      144
Local ring      125
Localization, finite      239
Localization, perfect      229
Lower continuous lattice      72
Maximal ring of quotients      200
Meet      63 64
Minimal ideal      24
Modular lattice      65
Module      5
Module of finite length      68
Module of fractions      57
Module of quotients      197
Module, $\mathfrak{F}$ -closed      198
Module, $\mathfrak{F}$ -discrete      145
Module, $\mathfrak{F}$ -divisible      155
Module, $\mathfrak{F}$ -injective      198
Module, $\mathfrak{F}$ -noetherian      263
Module, $\mathfrak{F}$ -reduced      159
Module, $\mathfrak{F}$ -torsion      146
Module, $\Sigma$ -injective      264
Module, absolutely pure      48
Module, Artin — Rees      169
Module, Artinian      13
Module, codivisorial      267
Module, coherent      42
Module, cotertiary      161
Module, countercyclic      206
Module, cyclic      10
Module, divisible      22 58 141
Module, faithfully flat      48
Module, finitely generated      10
Module, finitely presented      10
Module, flat      33
Module, FP-injective      48
Module, indecomposable      10
Module, injective      20
Module, isotypic      164
Module, Noetherian      12
Module, projective      19
Module, pure-injective      48
Module, quasi-injective      158
Module, reduced      141
Module, S-injective      58
Module, semi-artinian      182
Module, semi-simple      23
Module, simple      13
Module, torsion      57
Module, torsionless      94
Module, $\mathfrak{F}$ -flat      212
Monoid      15
Monomorphism      6 45 83
Morita context      112
Morita equivalence      106

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