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Atiyah M.F., Macdonald I.G. — Introduction to commutative algebra
Atiyah M.F., Macdonald I.G. — Introduction to commutative algebra



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Название: Introduction to commutative algebra

Авторы: Atiyah M.F., Macdonald I.G.

Аннотация:

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.


Язык: en

Рубрика: Математика/Алгебра/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 128

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Additive function      23
Adic topology      105
Algebra      30
Algebra, homomorphism      30
Annihilator ideal      8 19
Artin — Rees lemma      107
Artinian, module      74
Artinian, module, ring      76
Boolean ring      11
Chain conditions      74
Chain of submodules      76
Cokernel      19
complete      105
Completion      102
Composition series      76
Constructible topology      48
Contraction      9
Dedekind domain      95
DIMENSION      90
Discrete valuation ring      94
Domain, integral      2
Domain, integral, principal ideal      5
Exact sequence      22
Extension of an ideal      9
Field      3
Field, residue      4 43
Filtration      105
Finite, A-algebra      30
Finite, A-algebra, type      30
Finitely-generated      30
Flat      29
Flat, faithfully      29
Fractions, ring of      36
Generators of a module      20
Grothendieck group      88
Height      120
Hensel’s Lemma      115
Hilbert basis theorem      81
Hilbert function      118
Hillbert NullsteUensatz      67 69 82
Ideal(s)      2
Ideal(s), coprime      7
Ideal(s), decomposable      52
Ideal(s), direct product of      7
Ideal(s), fractional      96
Ideal(s), generated by      5
Ideal(s), intersection of      6
Ideal(s), invertible      96
Ideal(s), maximal      3
Ideal(s), primary      50
Ideal(s), prime      3
Ideal(s), principal      11
Ideal(s), product of      6
Ideal(s), quotient      8
Ideal(s), sum of      6
Image      2
Integral, A-algebra      60
Integral, A-algebra, closure      60
Integral, A-algebra, element      59
Integrally closed domain      60
Kernel      2 18
Length      76
Limit, direct      32
Limit, direct, inverse      103
Local ring      4
localization      38
Modular law      6
Module(s)      17
Module(s), direct product of      20
Module(s), direct sum of      20
Module(s), faithful      20
Module(s), finitely-generated      20
Module(s), flat      29
Module(s), free      21
Module(s), graded      106
Module(s), homomorphism      18
Module(s), product of      19
Module(s), quotient      18
Module(s), sub      18
Module(s), sum of      19
Multiplicatively closed set      36
Nakayama’s Lemma      21
Nilpotent      2
Noetherian, module      74
Noetherian, module, ring      76
Normalization lemma      69
Parameters, system of      122
Poincare series      116
Primary, decomposition      51
Primary, decomposition, ideal      50
Prime ideal(s)      3
Prime ideal(s), associated      52
Prime ideal(s), embedded      52
Prime ideal(s), isolated      52
Radical, Jacobson      5
Radical, Jacobson, nil      5
Radical, Jacobson, of a submodule      57
Regular local ring      123
Ring      1
Ring of fractions      36
Ring, absolutely flat      35
Ring, boolean      11
Ring, discrete valuation      94
Ring, graded      106
Ring, homomorphism      2
Ring, local      4
Ring, quotient      2
Ring, semi-local      4
Ring, sub      2
Ring, valuation      65
Saturated      44
Scalars, extension of      27
Scalars, extension of, restriction of      27
Spectrum, maximal      14
Spectrum, maximal, prime      12
Support      46
Symbolic power      56
Tensor product, of algebras      30
Tensor product, of modules      24
Torsion, element      45
Torsion, element, submodule      45
UNIT      2
Valuation ring      65
Varieties, affine algebraic      15
Zariski, ring      114
Zariski, ring, topology      12
Zero-divisor      2
Zorn’s Lemma      3
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