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Grillet P.A. — Abstract Algebra
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Название: Abstract AlgebraАвтор: Grillet P.A. Аннотация: About the first edition:
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-nd editionГод издания: 2007Количество страниц: 669Добавлена в каталог: 01.06.2008Операции: Положить на полку |
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Group, cyclic 14 21 24 25 35 46 68 94 100 507 Group, defined by generators and relations See presentation Group, derived 83 84 Group, dihedral 9 14 19 20 26 34 37 68 88 Group, finite 11 13 14 16 43—104 Group, free 29 27—31 505—506 Group, fundamental 8 18 20 37 43 83 Group, general linear 76 81 Group, generated by 33 Group, generated by a subset 14 Group, indecomposable 47 49 Group, isomorphic 20 Group, Klein four 9 13 44 Group, metabelian 83 Group, nilpotent 89 89—92 Group, p- 45 57 64 67 84 91 Group, profinite 204 434 Group, projective special linear 78 81 82 Group, quaternion 35 Group, quotient 20 20—23 Group, simple 73 73—76 81 82 Group, solvable 83 83—88 219 391 Group, special linear 77 77—82 Group, symmetric 8 58—64 88 Group, transitive 75 Group, value 248 Grps 583 Hall theorems 86—88 Hall, P. 86 Halmos, P. 640 Hamilton, W.R. 37 105 515 Haupidealsatz 303 Hausdorff, F. 628 Height of prime ideal 303 304 303—306 Helder’s theorem 100 Hensel, K. 243 261 Hensel’s Lemma 263 264 270 Hilbert basis theorem 147 Hilbert theorem on syzygies 511 Hilbert, D. 105 147 218 307 510 511 Hilbert’s Nullstellensatz 307 308 Hilbert’s Theorem 90 218 Hoelder, O. 74 100 Hom 415 415—423 433 442 589 Homology 463—471 Homology, singular 463 Homomorphism of algebras 382 516 Homomorphism of bimodules 418 Homomorphism of direct systems 423 Homomorphism of fields 117 156 Homomorphism of graded algebras 517 Homomorphism of groups 18 18—25 Homomorphism of inverse system 430 Homomorphism of lattices 542 Homomorphism of modules 320 320—324 Homomorphism of rings 107 112—115 Homomorphism of rings with identity 107 Homomorphism of T -algebras 614 Homomorphism of universal algebras 560 Homomorphism theorem for algebras 516 Homomorphism theorem for complexes 470 Homomorphism theorem for fields 156 Homomorphism theorem for graded algebras 517 Homomorphism theorem for groups 23 Homomorphism theorem for lattices 542 Homomorphism theorem for modules 322 Homomorphism theorem for rings 114 Homomorphism theorem for universal algebras 562 Homomorphism theorem in abelian category 603 Homomorphism, boundary 463 464 Homomorphism, central 516 Homomorphism, coboundary 463 467 Homomorphism, connecting 465 466 469 478 484 485 Homomorphism, evaluation 122 128 448 Homomorphism, inclusion 18 113 156 561 Homomorphism, K - 158 Homomorphism, natural 417 Homotopic 465 Homotopy 465 470 Hopkins — Levitski theorem 379 Hopkins, C. 379 Hopkins’s theorem 379 Hull, injective 410 408—410 Hurewicz, W. 393 Ideal 110 516 552 Ideal of quotient ring 114 Ideal of semigroup 578 Ideal, 275 Ideal, associated prime 276 Ideal, fractional See fractional ideal Ideal, generated by 293 Ideal, generated by monomials 149 Ideal, generated by subset 110 Ideal, graded 517 Ideal, irreducible 275 Ideal, left 318 Ideal, maximal 111 117 134 282 301 308 Ideal, membership problem 150 Ideal, minimal left 360 Ideal, nil 377 Ideal, nilpotent 376 Ideal, of 110 117 Ideal, order 632 551 Ideal, primary 275 287 Ideal, prime 117 133 274 281—282 287 298 302—306 Ideal, principal 110 552 Ideal, proper 110 Ideal, right 318 Ideal, semiprime 275 308 Ideal, two-sided 318 516 Idempotent 370 376 377 Idempotent, central 557 Identity See also identity element Identity element 2 Identity element of ring 106 Identity element, left 12 Identity of type T 566 Im, image 19 113 321 Image 603 Image of homomorphism 19 113 321 Image, direct 18 113 321 563 Image, homomorphic 568 Image, inverse 18 113 321 563 Indeterminate 120 126 130 131 INDEX 16 17 Index of centralizer 56 Index of normalizer 65 Index of stabilizer 55 Index, nilpotency 90 Index, ramification 258 258—261 Induction, Artinian 627 Induction, Noetherian 626 Induction, ordinal 635 635—639 Induction, strong 627 636 Induction, transfinite 629 Infimum See greatest lower bound Injection to coproduct 594 Injection to direct sum 325 Injection to free group 29 Injection to free product 40 Injection to group extension 95 Injection to semidirect product 93 INTEGER 1 Integer, algebraic 109 283 297 297—300 Integer, Gauss 109 137 Integer, modulo n 21 114 Integer, p-adic 245 246 266 Intersection of congruences 562 Intersection of ideals 110 Intersection of primary ideals 275—276 Intersection of subalgebras 560 Intersection of subgroups 15 Intersection of submodules 318 Intersection, reduced 276 interval 548 557 Inverse limit 431 429—434 Inverse limit of exact sequences 432 Inverse limit of modules 431 432 Inverse limit of sets 433 Inverse limit of universal algebras 574 Inverse of element 8 Inverse of product 10 Inverse, left 12 Isometry 9 Isomorphism 584 602 Isomorphism of algebraic varieties 313 Isomorphism of categories 588 Isomorphism of fields 156 Isomorphism of groups 20 Isomorphism of lattices 542 543 Isomorphism of modules 320 393 Isomorphism of partially ordered sets 633 542 Isomorphism of rings 107 Isomorphism of totally ordered abelian groups 251 Isomorphism of universal algebras 561 Isomorphism Theorems for groups 23—26 Isomorphism Theorems for modules 323 Isomorphism Theorems for rings 115 Isomorphism theorems for universal algebras 563 Isomorphism theorems, first 25 Isomorphism theorems, second 25 Isomorphism theorems, third 25 Isomorphism, K - 160 Isomorphism, natural 587 Jabobson density theorem 371 373 Jacobson, N. 370 372 376 377 Jech, T. 581 631 640 Join See least upper bound Jordan block 345 Jordan form 345 342—346 Jordan — Hoelder theorem 74 348 Jordan, C. 74 342 Kempf, G. 166 ker , kernel 19 113 321 Ker, equivalence relation 561 Kernel 602 Kernel of homomorphism 19 113 321 396 593 Klein, F. 1 Kramer, D. viii Kronecker, L. 45 Krull intersection theorem 301 Krull, W. vii 48 105 203 251 300 301 303 304 305 Krull-Schmidt theorem 50 349 Krull’s Hauptidealsatz 303 305 Krull’s Theorem 203; 305 Kuerschak, J. 243 Kuratowski, C. 628 l.u.b See least upper bound Lagrange, J. 1 Lagrange’s Theorem 16 Lasker, E. 273 Lattice 541 539—558 573 576 624 Lattice of normal subgroups 548 Lattice of subgroups 548 552 553 Lattice of submodules 546 Lattice of subsets 539 540 549 553 554 Lattice, Boolean 554 553—558 573 624 Lattice, complete 543 543—545 Lattice, complete Boolean 557 Lattice, distributive 549 549—553 577 624 Lattice, generalized Boolean 557 Lattice, modular 545 545—548 573 624 Lattice, subdirectly irreducible 576 Laurent series 131 131—133 245 254 Laws, absorption 542 Lazard, D. 450 455 Lazard’s theorem 455 LCM 135 Length of module 348 Length of normal series 70 348 Lift 402 471 472 477 Light’s test 5 35 Light’s test, fails 5 Light’s test, passes 5 LIMIT 592 591—593. Limit of sequence 233 243—245 247—248 268 462 Limit, directed See inverse limit Limit, finite 598 Limit, inductive See direct limit Limit, inverse See inverse limit Limit, projective See inverse limit Limit, standard 596 localization 287 285—290 Louis XIV 633 Lying over 281 282 MacLane, S. vii 184 188 393 463 490 500 532 581 609 MacLane’s theorem 188 532 MacNeille, H. 544 MacNeille’s theorem 544 Malcev’s theorem 580 Mal’cev, A.I. 580 MAP See also mapping Map, closure 543 Map, tensor 434 436 444 Mapping 582. See also multilinear mapping Mapping, biadditive balanced See bihomomorphism Mapping, bilinear 434 435 Mapping, middle linear See bihomomorphism Mapping, n -linear See multilinear mapping Mapping, order preserving 542 Mapping, polynomial 312 Mapping, regular 312 Maschke, H. 383 Maschke’s Theorem 383 506 Matrix of homomorphism 332 450 Matrix, column finitary 334 McCarthy, P. 203 Meet See greatest lower bound Metatheorem 540 585 Module 278 279 315—366 615. Module of finite length 348 379 Module of fractions 442 456 Module over a PID 336—342 Module over polynomial rings 342 350 510—514 Module, Artinian 300 348 Module, blown-up 457 Module, complete 458 Module, completely reducible 363 Module, cyclic 318 323 Module, divisible 405 Module, double dual 448 Module, dual 419 448 448—451 Module, faithful 317 Module, finitely generated 274 318 Module, finitely presented 453 453—455 Module, flat 450 450—456 461 495 496 Module, free 330 329—338 Module, homology 464 Module, indecomposable 349 Module, injective 403 403—410 412 414 420 422 429 452 484 491 492 Module, left 315 Module, Noetherian 296 347 Module, projective 402 401—403 411 419 448—451 480 486 491 492 494 Module, quotient 279 Module, right 317 Module, semisimple 363 362—364 371 379 Module, simple 359 360 Module, torsion 339 Module, torsion-free 339 Module, unital 315 317
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