Serre J.-P. — Local Algebra - Multiplicities :: Электронная библиотека попечительского совета мехмата МГУ

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Serre J.-P. — Local Algebra - Multiplicities

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Название: Local Algebra - Multiplicities

Автор: Serre J.-P.

Аннотация:

This is an English translation of the now classic "Algèbre Locale - Multiplicités" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Tor-formula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 110

Добавлена в каталог: 19.06.2008

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Предметный указатель

Acyclic complex on a module      52
Additivity formula      100
Annihilator      4
Artin — Rees theorem      17
Artinian (ring)      21
Associated prime ideal      6
Associativity formula      114
Auslander theorem      71
Auslander — Buchsbaum theorem      78
Basic degrees      92
Binomial polynomials      19
Canonical topology      19
Chain of prime ideals      29
Chain of prime ideals, extremity      29
Chain of prime ideals, length of      29
Chain of prime ideals, maximal      45
Chain of prime ideals, origin      29
Chain of prime ideals, saturated      45
Codifferent      40
Cohen — Macaulay module      63
Cohen — Seidenberg first theorem      31
Cohen — Seidenberg second theorem      32
Cohen's theorem      80
Cohen-Macaulay ring      63
Completed tensor product      102
Completed Tor      102
CYCLE      99
Cycle, direct image      117
Cycle, intersection      117
Cycle, positive      99
Cycle, pull-back of      118
Cycle, rational over a field      116
Cycles, reduction of      120
Dedekind ring      39
Depth      61
Difference operator      20
Dimension of a module      33
Dimension of a ring      29
Direct image (of a cycle)      117
Discrete valuation ring      37
Divisorial ideal      39
Domain      1
Embedded prime ideal      8
Equal characteristic      106
Essential prime ideal      10
Euler — Poincare characteristic      56
Factorial ring      39
Filtered module      11
Filtered ring      11
Finite length      6
Flat module      2
Global homological dimension      70
Graded module      14
Graded ring      14
Graded-free      91
Graded-polynomial algebra      92
Height      29
Higher Euler — Poincare characteristics      57 88 111
Hilbert polynomial      22
Hilbert theorem      22
Homological dimension      70
Ideal of definition      33
Induced filtration      11

Injective dimension      70
Integer-valued polynomial      20
integral      30
Integral closure      32
Integrally closed      32
Intersect properly      112
Intersection cycle      117
Irreducible      4
Irreducible component      5
Jacobson radical      1
Koszul complex      51
Krull theorem      37
Lie over      31
Local ring      1
m -adic filtration      12
m-adic topology      12
m-sequence      59
Maximal ideal      1
Minimal free resolution      84
Minimal homomorphism      84
Multiplicity      100
Nakayama's lemma      1
Noetherian module      4
Noetherian ring      4
Non-singular variety      82
Normal ring      37
Normalization lemma      42
Nullstellensatz      44
Poincare series      92
Polynomial-like function      21
Primary (submodule, ideal)      10
Primary decomposition      10
Prime ideal      1
Product formula      115
Projection formula      118
Projective dimension      70
Proper intersection      112
Pseudo-reflection      95
Pull-back (of a cycle)      118
q-good (filtration)      17
Quotient filtration      11
Radical      3
Reduction to the diagonal      49 101 115
Reflexive module      78
Regular ring      75
Regular system of parameters      78
Right interior product      87
Samuel polynomial      24—25
Samuel theorem      24
Semilocal ring      1
Shephard — Todd theorem      95
Shift      52
Spectrum      4
Strict morphism (of filtered modules)      12
Support (of a module)      5
Symbolic power (of a prime ideal)      38
System of parameters      36
Tor-formula      112
Unramified (local ring)      108
Weil theorem      116
Zariski ring      19
Zariski topology      4
Zero-divisor (in a module)      53

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