√лавна€    Ex Libris     ниги    ∆урналы    —татьи    —ерии     аталог    Wanted    «агрузка    ’удЋит    —правка    ѕоиск по индексам    ѕоиск    ‘орум   
blank
јвторизаци€

       
blank
ѕоиск по указател€м

blank
blank
blank
 расота
blank
Reid M. Ч Undergraduate commutative algebra
Reid M. Ч Undergraduate commutative algebra

„итать книгу
бесплатно

—качать книгу с нашего сайта нельз€

ќбсудите книгу на научном форуме



Ќашли опечатку?
¬ыделите ее мышкой и нажмите Ctrl+Enter


Ќазвание: Undergraduate commutative algebra

јвтор: Reid M.

јннотаци€:

These are notes from a commutative algebra course taught at the University of Warwick several times since 1978. In addition to standard material, the book contrasts the methods and ideology of abstract algebra as practiced in the 20th century with its concrete applications in algebraic geometry and algebraic number theory.


язык: en

–убрика: ћатематика/јлгебра/”чебники/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1995

 оличество страниц: 164

ƒобавлена в каталог: 18.03.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
blank
ѕредметный указатель
$S^{-1}$ is exact      90Ч92
$\mathbb Z$ versus $k[X]$      5Ч10 22
$\mathrm{Spec}\mathbb{Z}[Y]$      25
1-dimensional local integral domain      115
a.c.c. (ascending chain condition)      11 13 49 52 56 109
Abstract versus concrete      11 12 23 49 51 95 115 136
Algebraic curve      7 11
Algebraic number theory      8Ч11 16Ч18 25 58 112
Algebraic variety      see variety
Algebraically closed field      3 70
Algebraically independent elements      63
Algebraically nonclosed field      72 73 82
Anal germs      33 35 52 112 127
Analytic arc      127
Annihilator Ann^ M      96
Artinian local ring      56
Artinian module      56
Artinian ring      51 55 56
Assassin Ass M      98Ч109
Associated prime Ass M      98
Axiom of Choice      25 26 36 50 56
Basis of free module      40
Bourbaki, Nicholas      95 98
Cayley Ч Hamilton theorem      41Ч43 47
Chain conditions      11 18 26 49Ч53 76 103 108
Characteristic char k      7
Codimension      1
Codimension, prime ideal      see minimal nonzero prime ideal
Codimension, subvariety      5 112 121
Cokernel coker $\varphi$      45
Completion of DVR      126
Composite valuation      118 127
Coordinate ring k[V]      3 12 70 80 92 121
Correspondences V and I      72
Cusp $Y^2 = X^3$      7Ч8 11 62
Cyclic module      41
d.c.c. (descending chain condition)      51 56
Dedekind domain      134
Determinant trick      41Ч44 60 116
Devissage      103
DIMENSION      115
Dimension theory      2 131
Direct sum of modules      40 45 53Ч54
Direct sum of rings $A_1\oplus A_2$      2 4 28Ч29
Disassembling a module      103 111
Discrete valuation      113
Division with remainder      6 14 16
DVR (discrete valuation ring)      12 112Ч117 119Ч123
Easy Nullstellensatz      31 73 78 81
Elementary symmetric functions      68 124 125
Empty set theory      20 36
Endomorphism of module      38 41Ч43
Equal characteristic      7
Euclidean ring      6 14 16Ч18
Evaluation map $f\mapsto f(P)$      3 21 35 36 70Ч72 78 81
Exact sequence      44Ч48 54
Existence of assassin      99 102 115
Existence of maximal ideals      26
Existence of primary decomposition      106 108Ч109
Existence of prime ideals      25Ч27
f.g. (finitely generated) algebra      49 55 63 70 75 80
Factorisation      2Ч3 10 18 95
Faithful A-module      38
Field extension      15 25 58 62 66Ч67 82 122
Field of fractions K = Frac A      2 84
Finite A-algebra      53 58Ч61 63 69 93 122Ч124
Finite and integral      58Ч61 68
Finite branched cover      132
Finite module      40 43Ч44 47 53Ч54 123
Finitely generated ideal      49Ч51
Finiteness conditions      40 49 58Ч60
Finiteness of normalisation      13 122Ч124 136
Fitting's lemma      56 109 111
Formal power series ring $A[x]$      16 32 56 127 130
Free module      40Ч41
Function field k(V)      92 93
Galois theory      10 14 72 82 123
Gauss' lemma      15 22
Generators of module      40 43
Geometric ring      80
Geometric view      1 3Ч5 12 21 23Ч25 29 70 78 106
Geometry      70 75 95
Geometry of Spec A      77Ч82 97
Germ      33 52
Golden ratio $\tau$      18 59 67
Hilbert basis theorem      49 54Ч56
Hilbert, David      11 49
history      11 49 142Ч144
Homological algebra      48
Hypersurface $V(F) \subset k^n$      3
Ideal      19
Ideal, in localisation      87 109
Ideal, maximal      see maximal ideal
Ideal, of denominators      119
Ideal, prime      see prime ideal
Idempotent      2 4 28
Image $\mathrm{im}\varphi$      38 44
Indecomposable ideal      108Ч109
Inseparable field extension      128 137
Integral algebra      59
Integral and finite      58Ч61 68
Integral closure $\tilde A$      61
Integral dependence      58
Integral domain      2 99
Integral element over A      58Ч61
Integral extension      59
Integrally closed      61
Intersection of DVRs      12 121Ч122
Intersection of minimal prime ideals      29 77 79
Intersection of prime ideals      28Ч30 95 105
Invertible element      2 26 86
Irreducible components      28Ч29 76Ч77 82 95 101 106
Irreducible element      2 8
Irreducible variety      74Ч75 82 83 92
Isomorphism theorem      38Ч39 48
Kernel $\mathrm{ker}\varphi$      19 38Ч39 45
Koszul complex      46Ч47
Linear algebra      37 41
Local parameter of DVR      113
Local property      118
Local ring      2 31Ч33 35 47 82 84 88 112 118
Localisation $A_P$      31Ч32 82 84Ч92
Maximal condition      56
Maximal element      25 49 50
Maximal ideal      3 20Ч21 35 70 72
Maximal spectrum m-Spec A      21 80 119
Minimal element of Supp M      101
Minimal nonzero prime ideal      115 119Ч121
Minimal polynomial      15 124 125
Minimal prime ideal      28 79 95 98 105
Mixed characteristic      7 16
Module      37
Module, of fractions $S^{-1}M$      89Ч90 96
Monic polynomial      14 58 66
Multiplicative set      20 27Ч28 31 34 84Ч85
Nakayama's lemma      43Ч44 47 69
Newton's rule      125
Nilpotent      4
Nilpotent element      2 4 27Ч29 86 104
Nilpotent ideal      56
Nilradical nilradA      2 27 29 35 81
Noether normalisation      58 63Ч67 122 132
Noether, Emmy      11 49 63 95
Noetherian Induction      49Ч57 76Ч77 79 108
Noetherian module      52Ч54
Noetherian ring      49Ч51 54Ч57 95 99 135Ч141
Noetherian topology      76
Non-Noetherian ring      51
Noncommutative ring      37 38
Nonsingular      62 133
Normal integral domain      61 114
Normal Noetherian ring      118Ч122
Normalisation $\tilde A$      61Ч63 68 122Ч124 133
Nullstellensatz      3 5 31 58 70Ч75 80 82
Number field      62
Number field and algebraic curve      7Ч10 62Ч63
Number field and normal variety      112
Ordered group      116Ч118
Partially ordered set      13 25 36 49
Picture      13 29 121 141 146
PID (principal ideal domain)      13 14 22
Plane curve      7
Poles      see zeros and poles
Polynomial map      80 83
Polynomial ring $A[x_1, \ldots, x_n]$      3 15 35 49 55 63 106
Presentation of module      41 55
Primary decomposition      12 88 95Ч111 115
Primary ideal      95 103Ч111
Prime element      2
Prime element of DVR      113
Prime ideal      20Ч29 74 78 87 95 100
Prime spectrum      see spectrum Spec A
Primitive extension $K \subset K(\alpha)$      14 15 124
Primitive polynomial      15 22
Principal ideal      6 14 22 112 114
Product of ideals IJ      34
Quadratic number field $\mathbb Q(\sqrt{n})$      62 68
Quadratic reciprocity      16
Quadric cone      5 107
Quotient module M/N      38
Quotient ring A/I      20 91
Radical ideal I = rad I      30 77Ч78 95
Radical rad I      29 104
Radius of convergence $\rho$      33
Reduced ideal      80
Reduced polynomial      4 82
Reduced ring      27 35
Reducible variety $X=X_1\cup X_2$      4 74
Reduction to local ring      31 84 88 102 110 120
Regular local ring      131
Remainder theorem      14 36
Residue field at P      21 91
Resolution of singularities      13 62Ч63 133
Ring of analytic functions      35
Ring of fractions $S^{-1}A$      12 84Ч94
Ring of functions      1 12 52 80 81 89
Ring of germs      33
Ring of integers $\mathcal O_K$      8Ч10 13 16Ч18 58 62
Scheme theory      141
Separable field extension      122Ч126 128
Set theory      see Zorn's lemma
Short exact sequence (s.e.s.)      45Ч47
Shortest primary decomposition      105
Singular plane curve      7 62
Snake lemma      48
Spec $\mathbb Z[X]$      22
Spectrum Spec A      12 21Ч25 75 77Ч82 115 130
Split exact sequence      45Ч46 48
Strongly coprime ideals      34
Subring $A' \subset \mathrm{End} M$      38 42Ч43
Subvariety      4
Support Supp M      96Ч98 100Ч103
Tangent plane      5
Taylor series      29 130
Total order      116Ч117
Trace $Tr_{L/K}$      123Ч126
Transfinite induction      25 36
UFD (unique factorisation domain)      3 13Ч15 18
UFD is normal      15 62
UMP (universal mapping property)      14 86 93Ч94
Unequal characteristic      7
Unique factorisation      2Ч3 14
Uniqueness of primary decomposition      109Ч110
UNIT      2 26 86
Vacuity      20 36
Valuation ring      113 116Ч118
Value group of valuation      117
Variety $V \subset k^n$      3 11 70Ч77 80 89 92 121
Variety $\mathcal V(I)\subset \mathrm{Spec}\, A$      78Ч79 96Ч97
Weak Nullstellensatz      3Ч5 67 70Ч72
Weight of monomial w(Ym)      65
Zariski topology      75Ч81 83 96Ч97 100 130
Zerodivisor      1Ч2 4 28Ч29 79 84 85 92
Zerodivisor, for M      95 96 100
Zeros and poles      12 112 121
Zeros theorem      73
Zorn's lemma      13 25Ч27 36 56
blank
–еклама
blank
blank
HR
@Mail.ru
       © Ёлектронна€ библиотека попечительского совета мехмата ћ√”, 2004-2019
Ёлектронна€ библиотека мехмата ћ√” | Valid HTML 4.01! | Valid CSS! ќ проекте