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Matsumura H. — Commutative algebra
Matsumura H. — Commutative algebra

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Название: Commutative algebra

Автор: Matsumura H.

Аннотация:

This book has evolved out of a graduate course in algebra I gave at Brandeis University during the academic year of 1967-1968. At that time M. Auslander taught algebraic geometry to the same group of students, and so I taught commuratire algebra for use in algebraic geometry. Teaching a course in geometry and a course in eommutative algebra in parallel seems to be a good way to introduce students to algebraic geometry.
Part I is a self-contained exposition of basis concepts such as flatness, dimension, depth, normal rings, and regular local rings.
Part II deals with the finer structure theory of noetherian rings, which was
initiated by Zariski (Sur la normalit6 analytique des vari6t6s normales, Ann. Inst.Fourier 2 1950) and developed by Nagata and Grothendieck. Our purpose is to lead the reader as quickly as possible to Nagata's theory of pseudo-geometric tings (here called Nagata rings) and to Grothendieck's theory of excellent rings.
The interested reader should advance to Nagata's book LOCAL RINGS and to Grothendieck's EGA, Ch. IV.
The theory of multiplicity was omitted because one has little to add on this subject to the lucid expositoh of Serre's lecture notes (Algebre locale. Multiplicite, Springer-Verlag). Due to lack of space some important results on formal smoothness (especially its relation to flatness) had to be omitted also. For these, see EGA. We assume that the reader is familiar with the elements of algebra (rings, modules, and Galois theory) and of homological algebra (Tot and Ext). Also, it is desirable but not indispensable to have some knowledge of scheme theory.


Язык: en

Рубрика: Математика/Алгебра/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1980

Количество страниц: 312

Добавлена в каталог: 17.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$ \kappa( )$      152
$ \Phi$      12
$Der_k(A,M)$      181
$\mathcal(L)()$      64
$\Omega( )$      2
$\Omega_{A/k}$      182
(SJ)      289
(WJ) (= weak jacobjan condition)      289
Adic topology      68 163
Almost integral      115
Analytically isomorphic      175
Analytically isomorphic unramified      234
Ann( )      8
Artinian ring      13
Artinian ring module      261
Ass( )      49
Associated prime      49
Cartier’s equality      279
Catenary      84
Characteristic      13
Co-primary (module)      52
Coefficient field      197
Coefficient field ring      210 268
Cohen — Macaulay (= C.M.)      106 110
complete      163
Complete intersection (=CI)      308
Completion      165
Constructible set      39
d( )      76
Dedekind domain      294
Depth      102
Der(A,M)      180
Derivation      180
Differential module      182
Differential module basis      271
DIMENSION      71 72
Dimension, formula      86
Dimension, inequality      86
Directed downwards      224
Elementary open set      2
Embedded prime      51
Excellent ring      259
Extension of ring by module      177
Faithful module      261
Faithfully flat      17
Fibre      153
Filtration      67
Finite presentation      7
Flat      17
Formally etale      273
Formally etale projective      215
Formally etale smooth      198
Formally etale smooth, relative to      222
G-ring      249
Generalization      45
Generic point      41
Geometrically regular      208
gl.dim      128
Global dimension      128
Going-down Theorem      31
Going-up Theorem      31
Grade      103
Graded ring      61
Graded ring, module      61
Height      71
Hilbert polynomial      67
Hilbert polynomial, characteristic function      67
Hilbert polynomial, syzygy theorem      132
Hilbert polynomial, zero point theorem      93
Hochschild extension      178
Homogeneous element      61
Homogeneous element, submodule      61
ht( )      71
Ideal of definition      73 164
Idealwise separated      145
Imperfection (module of)      278
Independent elements      299
Injectively free      228
Irreducible component      38
Irreducible component, element      141
Irreducible component, set      38
J-0, J-l, J-2      246
Jacobson radical      10
Japanese ring (= N-2)      231
Koszul complex      133
Krull dimension      71
Krull ring      293
Leading form      118
Lies over      2
Linear topology      161
Linearly disjoint      196
Local ring      9
localization      6
Locally closed      39
Maximal spectrum      2
Minimal basis      12
Minimal basis, homomorphism      113
Minimal basis, resolution      136
N-l, N-2, Nagata ring      231
nil( )      5
Noetherian module      261
Noetherian module, ring      13
Noetherian module, space      38
Non-degenerate homomorphism      60
Normal domain      115
Normal domain, ring      116
Normalization theorem      91
ord( )      118
Order      118
p-basis      184 269
p-degree      270
Presentation      7
Primary ideal      1
Primary ideal, decomposition      54
Primary ideal, submodule      52
Prime chain      71
Prime ideal      1
Pro constructible set, ind constructible set      39
Quasi coefficient field      274
Quasi coefficient ring      275
Quasi-coefficient field      274
Quasi-coefficient ring      275
Quasi-excellent ring      259
Quotient ring      6
Radical ideal      1
Radical of ring (= Jacobson radical)      10
Reduced ring      5
Reduced ring, polynomial      269
Regular element      12
Regular element, homomorphism      249
Regular element, local ring      78
Regular element, ring      140
Regular element, sequence      95
Regular element, system of parameters      78
Residue field      9
Ring of fractions      6
Semi-local ring      10
Separable algebra      193
Separably generated      190
Separating transcendency basis      190
Smooth      200
Specialization      45
Spectrum      2
Stable      45
Submersive      46
Supp( )      16
Support      16
Symbolic power      56
System of parameters      78
Total quotient ring      12
Trivial extension      178
UFD      141
Universally catenary      84
Universally Japanese ring      231
Unmixed ideal      110
Unmixedness theorem      110
V( )      2
Zariski ring      172
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