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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
Maple (computer algebra system)      375
Mapping cone      427 428 650
Mapping cone and double complexes      650
Mapping cones revisited      657
Mapping cones to spectral sequences      650
Maps and homotopies of complexes      627
Maps from power series rings      198
Maps from projective to acyclic complexes      491
Massey      657
Mathematica (computer algebra system)      375
Matrices of linear forms      604 606
Matroid      556
Max Noether's AF+BG theorem      466
max-Spec R, maximal spectrum      54
maximal Cohen — Macaulay modules      529 599
Maximal ideals      12 141
Maximal M-sequence      430
Maximal minors      463
Maximal regular sequences      424
Maximal spectrum (max-spec)      54
Maximal subfields      205
Menger, K.      214
Minimal complex      472
Minimal free resolution      478
Minimal free resolution is unique      490 491
Minimal generators of monomial ideal      320
Minimal Groebner basis      329 367
Minimal injective resolution      529 623
Minimal map      472
Minimal primary decomposition      95
Minimal prime      77
Minimal primes of I      47
Minimal resolutions      469
Minimal set of generators      472
Minor, $k\times k$      244
Minor, principal      369
Minors of a matrix      107 244 300 301 370 465 565
Minors, $2\times 2$      53
Miyata, T.      649
Model theory      142
Module of homomorphisms      318
Modules      15
Modules over a Dedekind domain      484
Moduli      38
Moebius, A.F.      39
Moller, H.M.      333
Monic polynomial      117 126 138
Monomial      13 139 319 349
Monomial basis      323
Monomial curve singularities      379
Monomial ideal      111 319 365
Monomial orders      323 324
Monomial submodule      319
Monomorphism      15
Mora, T.      333
Mori, S.      26 263
Morin, B.      403
Morphism      35 304 689 697
Mourrain, B.      371
Multilinear algebra      565
Multiple point on a line      178
Multiplicatively closed set      59 70
Multiplicity      259 274 276 277 300
Multiplicity in primary decomposition      102
Mumford, D.      38 505 506 516
Nagata rings      294
Nagata's altitude formula      289 299
Nagata's factoriality lemma      483
Nagata, M.      26 105 184 263 483
Nakayama's lemma      124 129 135 136 203 241 298 299
Nakayama's lemma, homological version      473
Natural transformation      689 690 698
Neighborhoods      57 156
Newton's method      183
Newton, I.      23 295 305
Nielsen, H.A.      591
Nilpotent      33 36 71
Nilpotents do not affect dimension      219
Nine lemma      635
Nodal plane cubic      185
Noether normalization      221 281 283 298 308 460
Noether normalization with separating transcendence base      401
Noether — Lefschetz theorem      515
Noether, E.      23 27 47 49 57 87 118 127 217 231 256 296 612
Noetherian      27 28 46 62 85 183 192 229 265 294 625
Nonconstructive fashion      317
Nonhomogeneous Grobner bases      372
Nonsingular      249
Nontrivial idempotent      85
Nonunique resolution      515
Nonzerodi visor      12 163
Normal cone      441
Normal cone of a regular sequence      441
Normal domain      118 251
Normal expression      349
Normal module      177
Normal ring      125 126 138 249 251 289
Normal vector field      177
Normalization      118 126 128 137 141 251 364
North pole      50
Nullstellensatz      31 33 38 131 141 311 413
Number theory      21
Numbers of generators of powers      276
Objects of a category      689
Obstruction to generating M      494
One-generic matrices      604 605
Open morphism      238 299
Orientation      434
Orthogonal idempotents      13 187
Orthonormal basis      466
Osculating plane      380
p-adic integers      184
p-adic numbers      179 182
p-adic unit      209
p-bases      559
p-basis      190
Parallel lines meet at infinity      39
Parameter ideal      234 235 272 275 278
Pardue, K.      348
Partitions      585
Partitions of unity      83
Pascal, B.      553
Pathologies      218 221 229
Peano, G.      214
Perfect fields      190
Perfect ideals      485
Periodic polynomial      245
Permutation of a regular sequence      422
Perpendicular subspace      444
Persymmetric matrix      604
Peskine and Szpiro      498 539
Peskine, C.      334 540 591
Pfaff $\varphi$, Pfafnan (square root of determinant)      588
Pfaffians      463 503 588
Pic(i2), group of isomorphism classes of invertible ideals      255
Picard group      255 258
Pit      260; see Principal ideal theorem
Pluecker, J.      24 39
Poincare, H.      213 612
Points at infinity      40
Pole, order of a      246
Polynomial equations      34
Polynomial function      31 33
Polynomial map      35
Polynomial ring      394
Polynomial with periodic coefficients      245 280
Polynomial, factoring      305
Portnoy's Complaint      709
Positive characteristic, further readings      710
Positive cone      366
Power series      205
Power series ring      189 193 198
Pragacz, P.      591
Priddy's generalized Koszul complex      444 445
Priddy, S.      338
Primary component      95
Primary decomposition      23 87 94 363 477 710
Primary decomposition and projective dimension      477
Primary decomposition, (non)-uniqueness of      102
Primary decomposition, geometry of      103
Primary decomposition, uniqueness of      111
Primary ideal or submodule      94 111
Prime avoidance      90 113
Prime element      14
Prime ideal      12 54 60 70 111 243
Prime in a graded ring      297
Primes in an integral extension      129
Primes in polynomial rings      297
Primes, minimal over I      47 90
Primitive polynomial      109
Principal ideal domain      13 54 137 163
Principal ideal ring      228
Principal ideal theorem      231ff
Principal ideal theorem for depth      449
Principal ideal theorem, converse to      233
Problems in computation      364
Products of algebraic sets      299
Products of domains      78
Products of rings, expression by idempotents      85
Projection from a product to a factor      299 304 318
Projection to a quotient      37
Projective algebraic set      40
Projective closure      41 359
Projective closure by saturation      372
Projective dimension      469 470
Projective dimension and associated primes      477
Projective dimension and depth      451 475
Projective dimension and primary decomposition      477
Projective geometry      51
Projective module      136 137 265 267 364 471 615
Projective modules, characterization of      616
Projective morphism      166
Projective of constant rank      493 496 513
Projective plane, complex      215
Projective products      299
Projective r-space      39
Projective resolution      469 626
Projective resolution functor      682
Projective varieties      39 304 464
Proper ideal      12
Proper morphism      118 129 166 300 305 315
Pseudo-reflection      48
Pseudogeometric      192
pth power map      201
Puiseux, V.      295
Pullback      362
Pure codimension 1      257
Pure transcendental extension      555
Q, rational numbers      12
Quadratic algebra      444
Quadratic relations      444
Quadric, rank of      467
Quadrics      51 459 466
Quasi-isomorphism of complexes      655 680
Quaternions      482
Quick and dirty proof of the Nullstellensatz      142
Quillen, D.      386 481
Quism      482; see quasi-isomorphism
Quotient by a group      37 296 297
Quotient by an ideal (I:J), computing      15 374
Quotient on division      320
R, real numbers      12
R-bilinear      160
R-linear      691
R-sequence      241
R0      252 266
R1      252
Rabinowitch's trick      132 142
rad /, radical of an ideal      71
Radical      33 71 111 137
Radical complete intersection      415
Radical of an ideal, computing      363
Rank of a module      16 135 261
Rank of a quadric      467
Rank of an ideal, synomym for codimension      226
Rao, A.P.      540
Rational convex polyhedral cone      464
Rational curves, computer project      378
Rational function      251 555
Rational map      266
Rational normal curve      380 587 606 650
Rational quartic in $P^3$      466
Ratliff, L.      289
Reduced Groebner basis      329 367
Reduced ring      33 251 266 562
Reduction to the diagonal      277 299—301
Reduction to the join      301
Reductive group      584
Rees algebra      167 342
Rees, D.      591
Refined by      326
Reflection of isomorphism      203
reg M, Castelnuovo — Mumford regularity      505
Regular function      33 251
Regular in codimension 1      249 266
Regular local ring      191 240 469 474 484
Regular local ring is factorial      483
Regular local ring, Jacobian criterion for      402
Regular local rings and regular sequences      465
Regular local rings are Cohen — Macaulay      462
Regular map      35
Regular parameter      247
Regular sequence      173 241 243 246 419 426 437 441 465
Regular sequence in any order, generation by      438
Regular sequences and flatness      468
Regular sequences permutability      422 438
Regular sequences, characterization of      517
Regular system of parameters      240
Regularity and hyperplane sections      508
Regularity of generic initial ideals      509
Regularity, Castelnuovo — Mumford      378 505 516
Relative cotangent bundle      389
Relative cotangent sequence      386
Relative tangent bundle      389
Remainder on division      330
Removable singularities theorem      251
Representable functors      695
Representation theory of GL(V), SL(V)      566 584
Representation theory, success of      479 480
Residue class field      60
Residue map      548
Resolution      617 626
Resolution of an ideal from a factor ring      654
Resolution of singularities      249
Resolutions and linkage      552
Resolutions of complexes      676
Restricted tensor product      392 705
Resultant, Sylvester's      307
Retraction      206
Reverse lexicographic deformation of 3 points      346
Reverse lexicographic deformation of conic      347
Reverse lexicographic order      326 328 339 344
Riemann sphere      215
Riemann surfaces and algebraic curves      215
Riemann — Roch theorem      44 456
Riemann, G.B.      24 215
Right adjoint      691
Right exact      65
Right exact functor      636
Right exact sequence      63
1 2 3 4 5
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