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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
Ring      11
Ring homomorphism      12
Ring of invariants      371
rlex, monomial order      326
Roberts, J.      463
Root      117 183
Roots in the p-adic numbers      209
Roth, P.      709
Ruckert, W.      217
s-degree      359
s-homogenization      359
S1      252 266
S2      252
Sagbi base      371
Saint — Donat, B.      464
Samuel, P.      271
Saturated chain condition      453
Saturation      360
Saturation $(I : J^{\infty})$      318
Scalars      13 317
Schanuel's lemma      490 635
Scheme      442
Schreyer, F.-O.      334 338 591
Schur functors      584 585
Schur, I.      584
Scripts, in Macaulay      375
Segre product      300
Seidenberg, A.      363 364
Self-duality of the Koszul complex      435
Self-injective      526
Semicontinuity, of fiber dimension      310 311
Semigroup rings      139 548
Semilocal      137
Separability      557
Separable      190 293 398 400 401 561 562
Separable but not separably generated      562
Separably generated      557
Separated      182 203 305
Separating transcendence base      401 561
Serre correspondence      436
Serre's criterion      249 266 403 457
Serre's intersection formula      640
Serre, J.-P.      119 274 279 300 477 480 525 527 643
Set theoretic complete intersection      364
Set theory      214
Sextuples of points in the plane      503
Sheaf      67 100
Sheaf cohomology      464
Sheaves on projective spaces      505
Shephard, G.C.      48
Short exact sequence      16 571
Short exact sequence of complexes      631
Sign convention      569
Simplicial complexes      612
Singular locus      402
Singular point      128
Skew-commutative algebra      423 479 566
Skew-symmetric      503 588
Smoothness      404—406 414
Snake lemma      634
Socle      522 523
Solution of polynomial equations      117 318
Spear, D.      338
Spec R, spectrum of R      54
Spectral sequence, collapse of      657
Spectral sequence, convergence of a      663
Spectral sequence, of a composite functor      670 677
Spectral sequence, of a double complex      665
Spectral sequence, of the exact couple      659
Spectral sequences      614 656
Spectrum of a ring (Spec R)      54
Split      16
Split = apparently split      649
Splitting criteria      81
Square roots of p-adic numbers      184
Square-free denominator      485
Stable nitrations      145 146
Stably free      480
Stalk of a sheaf      67
Standard bases      338
Standard expression      330
Stanley, R.      551
Stein factorization      118
Stillman, M.      334 351 354 509
Strands of the Koszul complex      591
Structure of modules      511
Stueckrad, J.      687
Submodule membership problem      371
Substitution      25
Summand      see Direct sum
Superheight      234 236
Supp M, support of a module      67
Support      67
Suslin, A.      481
Sylvester, J.J.      24 305 307
Symbol of a differential operator      547
Symbolic power      105 232
Symmetric algebra      565 569
Symmetric algebras, recognizing      575
Symmetric function      25
Symmetric power of an ideal      574
Symmetric semigroup      549
Symmetrization      578
Symmetry of diagonalization      578
System of divided powers      579
System of linear equations      612
System of parameters      222 231 234 235 246 301 437
Syzygies      318 332 366 377
Syzygy computation, easiest      370
Syzygy module      636
Syzygy theorem      44 474
Szpiro, L.      540
T, interchange map      577
Tangent bundle      383 388 393 436
Tangent bundles of spheres      481
Tangent cone      151 152
Tangent developable surface      380
Tangent vector fields      383
Tate, J.      143 479 580
Taylor complex      439
Taylor series as ring homomorphism      152
Taylor series, expansions (jet bundle)      408
Taylor, D.      439
Teichmuller, O.      559
Teissier, B.      403
Tensor      62
Tensor algebra      566 569
Tensor and hom      693
Tensor product      62 63 392 565—568
Tensor product of two complexes      427
Tensor products and Kaehler differentials      392
Term of a polynomial      13 320 349
Theology versus mathematics      26
Thie, P.R.      224
Thorup, A.      591
Three dimensions, meaning of      213
Tight closure      463
Todd, J.A.      48
Top of a module      522
Tor (derived functor of tensor)      159 363 639ff
Tor (derived functor of tensor) and flatness      171
Tor (derived functor of tensor) as an algebra      640
Toric varieties      464
Torsion      158
Torsion free      163 261 484
Total complex      652
Total quotient ring      60
Towber, J.      585
Trager, B.      363
Transcendence basis      556
Transcendence degree      215 216 221 285 400 555
Translation functor of a category      679
Triangulation of a category      679
Twist of a graded module      42
Twisted cubic curve      465 540 542
Ubiquity of Gorenstein rings      526
UFD      527; see factoriality
Ulrich, B.      545
Uniformizing parameter      247
Unions as colimits      701
Unipotent subgroup      349
Unique factorization      13 87 256
Uniqueness of minimal free resolutions      490 491
UNIT      11
Universal      698
Universal additive function      487
Universal hyperplane section      315
Universal property of localization      60 80
Universal R-linear derivation      384
Universally catenary      286 288 312 453
Universally Japanese rings      294
Unmixedness theorem, Macaulay's      456
Urysohn's lemma      55
Urysohn, P.S.      214
Uzkov, A.I.      57
Valuation      248 265
Valuation ring      264
Van der Waerden, B.L.      143
Varying with parameters      155
Vasconcelos, W.      363 364 440 501 517 518
Vector bundles      471
Vector bundles on an affine space      481
Verdier, J.L.      677
Veronese embedding      687
Veronese subring      228
Versal deformation      364
Vertex, of a cone      297
Vogel, W.      287 301 687
Volume of a neighborhood      224
Waldi, R.      519
Watanabe      510
Weakly m-regular      506 507
Weber, H.      24
Weierstrass, K.      24
Weight function      327
Weight of an exterior product of monomials      351
Weight order      327 331 367
Weil divisor      259
Weil, A.      306
Weyman, J.      585 591
What makes a complex exact      496
Wiegand, R.      484
Winkler, F.      334
Witt vectors      191 710
X/G, quotient by G      37
Yoneda's description of Ext      645 647
Yoneda's lemma      695
Z(I), zero locus      32 40
Z, integers      12
Z-graded rings and modules      30 81 138 287
Z/(2)-graded rings      30
Zacharias, D.      363
Zariski neighborhood      156 179
Zariski tangent space      176
Zariski topology      32 54 55 304 454
Zariski, O.      26 32 54 57 105 240 510 525
Zariski-closed set      54
Zero locus of a form in 4 variables = surface      215
Zero locus of a section of a vector bundle      443
Zero-dimensional Gorenstein ideals      376
Zerodivisor      12 90
Zorn's lemma      14 68 201 205
Z[i], Gaussian integers      21
1 2 3 4 5
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