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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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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 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
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