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Eisenbud D. — Commutative algebra with a view toward algebraic geometry
Eisenbud D. — Commutative algebra with a view toward algebraic geometry



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Название: Commutative algebra with a view toward algebraic geometry

Автор: Eisenbud D.

Аннотация:

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self- contained. Novel results and presentations are scattered throughout the text.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 797

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Compositum of subrings or subfields      557
Computation of differentials      387
Computation of Tor      160
Computation, further readings on      710
Computer algebra projects      375ff
Comultiplication      576
Conductor      268 549
Conductor square      268
Cone      287 297
Conies      51
Conjecture of Bass      485
Conjecture of Buchsbaum, Eisenbud, Horrocks      502
Connected components      85
Connected in codimension 1      454
Connecting homomorphism on homology      428 631
Conormal module      177 387
Conormal sequence      387
Conormal sequence of a complete intersection      440
Constant rank, projective modules of      493
Constructible algebraic set      309 311 315
Constructing prime ideals      85
Constructive module theory      318
Contragredient representation      521
Convergence of a sequence in the Krull topology      192
Convergence of a spectral sequence      663
Convergent power series      184
Converse of the Principal Ideal Theorem      233
Convex cone      139
Coordinate geometry      23
Coordinate ring      33
Coprimary module      94
Coproducts      699 700
Cotangent bundle      383 388
Cotangent bundle functor      386
Cotangent bundle of projective space      436
Counit of a coalgebra      576
Counting constants      232
Covariant functor      160
Criteria for flatness      161ff
Critical pairs in computation of Grobner basis      338
Cubic surface      504
Curve, Picard group of a      258
Cusp      51
de Rham complex      414 612
Dedekind domain      258 484
Dedekind, R.      22—24 87 256
Deformation, trivial      175
Deformations      175 176 410
Degree      44 300
Depth and codimension      448
Depth and dimension      686
Depth and flatness      460
Depth and localization      448
Depth and projection dimension      475
Depth and the vanishing of Ext      449
Depth is geometric      425
Depth of an ideal on a module      420 425 447
depth(I, M), length of maximal M-sequence      425
Depths of modules in an exact sequence      451
Derivations      383 583
Derived category      612 677 679
Derived exact couple      659
Derived functors      614 636
Desargues, G.      39
Descartes, R.      23 39 215
Descending chain condition      71
Descending chains of prime ideals      222 233
Descending multiplicative filtration      145
Determinant in multilinear algebra      565
Determinantal ideals, 106      112 244 371
Determinantal rings      463 710
Determinantal varieties      590 606
Determinate division      368
Determinate division algorithm      331
Devissage      308
Diagonal      300 576
Diagonal map      589
Diagram      697
Diagram of free modules over M      702
Diagrams and syzygies      634
Diameter and volume of a neighborhood      224
Differential basis      190 397
Differential module (=module with differential)      626
Differential modules, map of      627
Differential operator and inverse system      547
Differential operators      583
Differentials and colimits      394
Differentials and direct products      395
Differentials and localization      394
Differentials complete case      413
Differentials, Kaehler      383 611
dim, dimension      225
Dimension is a local property      218
Dimension of a graded ring      287
Dimension of a ring or module      43 213 225 246 555
Dimension of fibers      308
Dimension zero      227 546
Direct product      12 15 16 81 188 251 707
Direct product of Cohen — Macaulay rings      465
Direct sum, summand      15 31 47 571 700 707
Dirichlet, P.G.L.      22
Disconnected spectrum      85
Discrete valuation      248
Discrete valuation ring (DVR)      220 247 248 257 265 295
Disjoint union as colimit      707
Distinguished open set in Zariski topology      55
Distributive law      11
Divided Koszul relations      323 366
Divided power algebra      54 566 579
Divided powers and Pfaffians      588
Divided powers and the rational normal curve      587
Divisibility of binomials      352
Divisibility of monomials      320
Division algorithm      330 331
Division with remainder      318 330
Divisor      253 259 590
Divisors on a scroll      608
Divisors on rational normal curves      607
Dlementary symmetric function      25 296
Dlementary upper triangular matrices      349
Dolgachev, I.      503
Domain      12 150 166
Dominant morphism of varieties      288
Double complex      652
Double complex, third-quadrant      666
Double complexes with two rows      675
Dual socle generator      527
Duality      520 546
Duality for maximal Cohen — Macaulay modules      538
Dualizing functor      521 523 524
DVR      525; see discrete valuation ring
Eagon — Northcott complex      567 590 606
Eagon, J.      590
Eakin, P.      625
Eckmann and Schopf      621
Eclater      149
Effective methods in commutative algebra      318
Effectivity in the Nullstellensatz      34
Eilenberg — MacLane spaces      566
Eilenberg, S.      690
Eisenstein's criterion      466
Elimination of elimination theory      306
Elimination order      357 371
Elimination theory      303 304 314 318 356 357 365 372
Elimination theory, main theorem of      303 314
ellipse      52
Elliptic curves, further readings      710
Elliptic normal curve      608
Elliptic quartic      456
Embedded deformation      175
Embedded prime or primary component      90
End(I) = Hom(I,I), endomorphism ring      265
Endomorphism ring      521 524
Enumerative geometry      232
Epimorphism      15
Equation of integral dependence      118
Equational criterion for flatness      164
Equations of an image      358
Equicharacteristic      189 205
Essential extension      622
Essential submodule      523 622
Etale topology, further readings      710
Euclidean      214
Euler characteristic      44 501
Euler, L.      22 305
Evans, E.G.      377
Exact couple      657 658
Exact functor      520
Exact sequence      16 611 626
Exact sequence of terms of low degree      670
Exact sequences of complexes      631
Exact triangle      658
Exactness of a complex      496
Exactness of limits      196
Excellent rings      192 293 295
Exceptional fiber      276
Exceptional set      149
Exchange property      556
Existence of valuation rings      264
Ext (extension functor)      363 642 611ff 644
Ext (extension functor) as an algebra      647
Exterior algebra      432 565 569
Exterior power      136
Exterior power of an ideal      574
Factoriality      14 98 125 483 514 552
Factoriality, homological characterization      514
Factoriality, hypersurface rings      515
Factoriality, regular local rings      480
Factoring polynomials; Hensel's lemma and      184 206—208
Factorization of polynomials over Z and Q      138
Families of graded modules      175
Family of projective plane curves      172
Family of varieties or algebras      155
Fermat's last theorem      22
Fermat, P.      23 39
Fiber of a blowup      276
Fiber square      267
Fibers      155 227 286 303 308
Fiberwise characterization of projectives      513
Field      11
Field theory      555ff
Filtered colimit of free modules      703
Filtered colimits      701
Filtered colimits, exactness of      702
Filtered differential module      661
Filtered limits are not exact      708
Filtration, I-adic      145ff
Filtration, I-stable      146
Filtration, m-adic      181 192 664
Filtration, stable      661 664
Filtrations      145 146
Finite free resolutions      54 474
Finite global dimension      477
Finite group      38 467
Finite injective dimension      530 531
Finite map      227
Finite over R      122
Finite projective dimension      475 477
Finite resolution      470
Finitely generated      17 135
Finitely presented      17
Finiteness of the integral closure      292
First-quadrant double complex      666
Fitting invariant and annihilator      511
Fitting invariant or ideal      404 489 492 494 496
Fitting's lemma      493 590
Five lemma      524 635
Five points in $P^3$      370
Five-term exact sequence      670
Flags of linear subspaces      350
Flat modules as colimits of free modules      702
Flat modules, finitely presented      171
Flatness      66 68 137 155 163 165 183 237 303 342 703
Flatness and depth      460
Flatness and Hilbert functions      514
Flatness and regular sequences      468
Flatness of graded modules      174
Flattening stratifications      364
Flenner, H.      278
Forgetful functor      692
Form (= homogeneous polynomial)      13
Formal Nullstellensatz      49
Formal power series      179
Fourteenth problem, Hilbert's      26
Foxby, H.-B.      191
Fractional ideals      253
Fractions      59
Free algebra      692
Free and projective resolutions      617
Free module      16 615
Free presentation      17 492
Free product      707
Free resolution and associated primes      501
Free resolution of monomial ideals      439
Free resolutions      44 45 470 489 614
Free resolutions, linear      517
Function theory      23
Function, $C^{\infty}$      150 153
functor      62 689
Functoriality      570
Fundamental group, further readings      710
Fundamental problem of invariant theory      25
Gaeta, F.      542
Gaffney, T.      591
Galligo, A.      351
Galois theory      290 293
Gauss' fundamental theorem of algebra      31
Gauss' lemma      109 125 126
Gauss, C.F.      21—23 31 352
Gaussian integers      21
GCD, greatest common divisor      320
General change of coordinates      338
Generalized local rings      510
Generalized principal ideal theorem      244
Generators and relations      17
Generic codimension      466
Generic fiber      286
Generic flatness      307
Generic freeness lemma, Grothendieck's      303 307 308 315
Generic initial ideal      348 351
Generic initial ideal, existence      349
Generic matrix      300 371
Generic smoothness      404 406
Geometric invariant theory      37
Geometric nature of depth      426
Germ of a variety      67 151 153
Germain, S.      23
Ghost candy      656
Gianni, P.      363
Gilmer, R.      218
Gimigliano, A.      503
Gin(I), generic initial ideal of f      349
gl dim R, global dimension      472
Global dimension      470 474
Gluing      84
Going down      237 238 243 289
Going up      129 227
Gordan, P.      26 337 367
Gorenstein rings      525 528 536 537 541 542 545 553
Gorenstein, D.      525
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