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Matsumura H. — Commutative ring theory
Matsumura H. — Commutative ring theory



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Название: Commutative ring theory

Автор: Matsumura H.

Аннотация:

In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, Cohen-Macaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially self-contained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book.


Язык: en

Рубрика: Математика/Алгебра/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1986

Количество страниц: 320

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Rank 1, ordered group of      77
Rank of a module      84 154 159 163 166
Rational rank of ordered group      77
Reduced ring      3
Reduction of an ideal      112
Rees ring      120
Regular homomorphism      256
Regular local ring      x 105 138 153 156 163 187 236
Regular ring      157
Regular ring, geometrically      219 255
Regular sequence      x 123 188
Regular sequence, quasi-      124
Regular system of parameters      105
Residue field      3 23
Resolution of singularities      x 12 74 92 188
Rigidity conjecture      154
Ring of fractions      20 48
Samuel function      12 92 97 101 138
Samuel function of a regular local ring      106
Saturated (chain of prime ideals)      31
Saturation (of a multiplicative set)      23
Secondary module      42
Secondary representation      43
Semigroup      92
Semilocal ring      3 16 62 97 169
Separable algebra      198
Separable field extension      195 198
Separably generated      199
Separated I-adically ideal-      174
Separated module      55
Separating transcendence basis      199
Serre’s criterion for normality      183
Simple module      12
Skew derivation      285
Skew-commutative graded algebra      285
Smooth      193
Spectrum of a ring Spec A      20 24 35 48
Split cocycle      221
Split exact sequence      268
Split extension      191
Stably free module      161 163
Structure theorem for complete local rings      x 190 223 265
Support (of a module) Supp (M)      25 39 48 99
Symbolic power (of a prime ideal)      29 88
System of parameters      104
System of parameters, regular      105
Tensor product      26 45 53 266
Tensor product of complexes      127 281
topology      55
Tor      26 50 53 140 154 170 182 187 278
Total ring of fractions      21
Transcendence degree $tr. deg_t A$      32 118
Unequal characteristic      215
Uniformising element (of DVR)      79
Unique factorisation domain (UFD)      5 65 161
Unique factorisation into primes in a Dedekind ring      82
UNIT      1
Universally catenary ring      118 139 251
Unmixed      136 139
Unmixedness theorem      136
Unramified local ring      228
Valuation      75
Valuation ring      x 71
Valuation ring, composite of      72
Valuation, additive      75
Valuation, discrete      78
Value group of a valuation      75
Weak Jacobian condition (WJ)      239 259
Zariski ring      62
Zariski topology      25 29 36 74
Zariski — Riemann surface      73
Zero-divisor      38
‘Determinant trick’      7 81
1 2
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