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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
Gorenstein, Stanley's criterion for      551
goto      510
Govorov — Lazard theorem      166 703
Grade      425
Graded by degree      30
Graded canonical module      545
Graded case of linkage      552
Graded free R-module      44
Graded free resolution      45 470
Graded injective modules      624
Graded module      42
Graded primary decomposition      109
Graded ring      29 51 136 287
Graded rings, integral closure of      138
Grauert, H.      338 348
Greatest common divisor      320
Green's conjecture      381
Green, M.      443
Grell, H.      57
Griffith, P.A.      377
Grobner bases and flat families      342
Grobner basics      317 319 328 333
Grobner basis, computing a      368
Grobner basis, history of      337
Grobner basis, minimal      329 367
Grobner basis, simplest example      335
Grobner, W.      317 337
Grothendieck ring      265 303 308 403 519 677 695
Grothendieck, A.      118 293
Group, classical      463
Group, finite      467
Growth rate of a resolution, open problem on      364
Gruson, L.      334 591
Gulliksen, T.      479 580
Hairy ball and stably free modules      482
Hamilton, W.R.      119
Hartshorne's connectedness theorem      454 457
Hartshorne, R.      348 468 519 540
Hausdorff, F.      55
Heitmann, R.      484
Hemingway, Ernest      1
Hensel and Landsberg      24
Hensel rings, further readings      710
Hensel's lemma      179 180 183—185 200 201 206—209
Hensel, K.      179
Henselian      184
Henselization      184
Hermann, G.      363
Herzog, J.      191 440
Hilbert basis theorem      367
Hilbert function      42 43 53 148 223 245 318 470
Hilbert function and Grothendieck group      485
Hilbert function and polynomial, computing      355
Hilbert functions, characterization of      356
Hilbert polynomial      42 43 223 276 287 312 313 318 510
Hilbert polynomial is universal      487
Hilbert scheme      364
Hilbert series      245 280 487
Hilbert series is universal      487
Hilbert series of graded Cohen — Macaulay ring      550
Hilbert syzygy theorem      45 336 469 474
Hilbert — Burch theorem      501 502
Hilbert — Samuel function      272 275
Hilbert — Samuel polynomial      276
Hilbert's finiteness argument      47
Hilbert, D.      21 24 26 27 38 42 46 214 271 292 417 502 611 614
Hironaka, H.      338
Hirzebruch — Riemann — Roch formula      489
Hlex order      326
Hochster, M.      234 241 463 464
Hodge formula for singular cohomology      436
Homogeneous      13 30 52
Homogeneous, component      30
Homogeneous, coordinate ring      40 468
Homogeneous, coordinates      39
Homogeneous, ideal      30 366
Homogeneous, ideals, characterization of      81
Homogeneous, lexicographic order (hlex)      326
Homogenization      41 356
Homogenize      474
Homological methods      417
Homology      45 611
Homotopically trivial      655
Homotopies for the Koszul complex      432ff
Homotopy category of complexes      678
Homotopy equivalent      628
Homotopy of maps of complexes      492
Hopf algebra      566 576
Hopkins, C.      74
Horn (module of homomorphisms)      62 363
Horrock's conjecture      502
Huneke, C.      146 363 438 463 545 574
Hurwitz' theorem      206
Hyperbola      52
Hyperplane at infinity      41 359
Hyperplane section      447 508
Hypersurfaces      377
Ideal      12 22
Ideal at infinity      359
Ideal quotient      15 57 79
Ideal, membership problem      318 355 371
Ideals of minors      493
Ideals of monomials in a regular sequence      440
Idempotents      13 85 409 513
Identity element      11
Images      373
Imaginary points      39
Implicit function theorem      231
in(a), initial form of a      194
in(f), $in_>(f)$, initial form      325
Incomparability      131 227
Induced map on homology      627
Infinite free resolutions      710
Infinitesimal criterion of flatness      172
Infinitesimal deformation      410
Infinitesimal morphism      396
Infinitesimal neighborhood      219
Infinitesimal translation      396
infinity      39
Initial coefficient      27
Initial ideal      195
Initial term      27 48 152 325
Injective Abelian group      620
Injective dimension      529
Injective envelope      622 623
Injective envelope and primary decomposition      625
Injective graded modules      624
Injective hull      523 622
Injective modules      614 618
Injective modules over Noetherian rings      623
Injective objects, enough      621
Injective resolution      529 626
Injectives and primes      624
Integral closure      118 140 264 294
Integral closure of $Z[sqrt{n}]$      138
Integral closure of a graded domain      138
Integral closure of ideals      137
Integral dependence      117
Integral elements      118 120
Integral equation      118
Integral extension      118 123 130 227 228 289
Integral values, polynomial with      53
Intersection and product of ideals      639
Intersection multiplicity      300
Intersection theory, further readings      710
Intersections of ideals, how to compute      362 373
Invariant theory      24
Invariant theory, fundamental problem of      25
Invariants      47 48 463 467
Inverse      11
Inverse function theorem      180 184 208
Inverse limit      209; see limit
Inverse systems      526
Inverse systems and differential operators      547
Invertible      247 255 257 260
Invertible element      11
Invertible modules      253
Inverting an element of a ring      58
Involves a basis element      319
Irreducible algebraic set (variety)      32 88 314
Irreducible decomposition      96
Irreducible elements and prime elements      13 14
Irreducible ideal or submodule      96 111
Irreducible polynomials are prime      126
Irreducible representations of a group      584
Irreducible versus analytically irreducible      185
Irredundant primary decomposition      95
Irrelevant ideal      30
Isolated prime or primary components      90
Isomorphic      690
Isomorphism      15
Jacobi, C.G.J.      24
Jacobian criterion      402 403 457
Jacobian ideal      402 403
Jacobian matrix      402
Jacobson radical      124 136 203
Jacobson ring      131
Jacobson, N.      131
Jaffe, D.      364
Japanese rings      127
Japanese rings, universally      294
Jet bundle      408
Join variety      301
Jordan — Holder theorem      72
K(R), total quotient ring      60
K(x), Koszul complex      423
Kaehler differentials      384 408
Kaplansky, I.      115 419 438 471
Kapranov, M.      503
Kempf, G.      445 590
Kepler, J.      39
kernels      362 373
King of invariants      26
Kirby, D.      590
Kleiman, S.L.      510 591
Knuth — Bendix      338
Koh, J.H.      234
Koszul algebra      445
Koszul cohomology      443
Koszul complex      417 419 423 427 565 590 614
Koszul complex and cotangent bundle      436
Koszul complex and minimal free resolution      478
Koszul complex, duality      432
Koszul complex, tautological      443
Koszul complexes, tensor product of      428
Koszul homology      438
Kronecker, L.      22-24 232 417
Krull dimension      213 217 225
Krull intersection theorem      150
Krull intersection theorem, converse to      153
Krull rings      294
Krull topology      193 204
Krull — Akizuki theorem      263 264 294
Krull's principal ideal theorem (PIT)      222 231ff
Krull, W.      57 131 143 216 217 225 231 240
Kummer, E.E.      22 23
Kunz, E.      519 538
Lame, G.      22
Lang, S.      614
Larfeldt — Lech theorem      192
Lascoux, A.      591
Lasker, E.      22 23 87 226 256
Lattices      530
Laurent polynomials      82
Laurent series      295
Lazard, D.      703
Lazarsfeld, R.      334 591
LCM, least common multiple      320
Le Dung Trang      403
Least common multiple      320
Leedham — Greene, C.      258
Left adjoint      691
Left-derived functor      637
Left-exact functor      63
Left-exact sequence      63
Leibniz rule      383
Length      72 259 276
length M, length of composition series      72
Length of the chain      225
Leray spectral sequence      677
Levin      580
lex, hlex, rlex, characterization of      366
lex, hlex, rlex, monomial orders      326
Lexicogaphic product      326
Lexicographic deformation of 3 points      345
Lexicographic deformation of conic      346
Lexicographic order      48 326 344
liaison      350; see linkage
Lifting homomorphisms      360
Lifting idempotents      184 186 187 208
lim, colimit (or direct limit)      698
lim, inverse limit      181 697
Limit of a spectral sequence      656
Limits      181 192 196 697
Limits and adjoints      694
Limits and colimits are not exact      708
Linearly disjoint field extensions      557
Linearly reductive algebraic group      463
Linkage      520 539 544 552
Liouville's theorem      314
Lipman, J.      515 519
Local and graded      683
Local cohomology      100 649 683
Local cohomology and global cohomology      684
Local coordinate system      235
Local criterion for flatness      167 460
Local criterion for projectivity      616
Local duality      686
Local ring      12 57 60
localization      57 59 60 79 126 203 391
Localization of a complete intersection      484
Localization of a regular local ring      479
Localization of depth      448
Localization of graded rings      82
Localization of Kaehler differentials      409
Locally a complete intersection      462
Locally a domain      457
Locally closed      309
Locally free module      136 171 471
Locally trivial      156
Loefwal, C.      445
Long exact sequence of homology      632
Long exact sequence of Tor      160
Lucas, H.      352
Lying over      129
M(d), $d^{th}$ twist of M      42 321
m-regularity      505 507
m-regularity, weak      506 507
m-sequence      426
m/1, image of m in localization      59
Mac Lane, S.      557 559 690
Mac Laurin, C.      23
Macaulay (computer algebra system)      375
Macaulay's unmixedness theorem      456 590 606
Macaulay, and monomial orders      325—327 356
Macaulay, F.S.      226 463 525 526
MacRae, R.      514
Macsyma (computer algebra system)      375
Manin, Yu.      445
Map with finite fibers      219
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