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