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Eisenbud D. — Commutative algebra with a view toward algebraic geometry
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Название: Commutative algebra with a view toward algebraic geometryАвтор: 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: Рубрика: Математика /Алгебра /Алгебраическая геометрия /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1995Количество страниц: 797Добавлена в каталог: 12.03.2005Операции: Положить на полку |
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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), 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 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), 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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