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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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Schur, I. 102 360 380 Schur’s lemma 360 Schur’s Theorem 102 493 Section, lower 632. See also order ideal Semigroup 3 1—7 Semigroup, cancellative 577 Semigroup, commutative 3 577—579 Semigroup, determined by ideal 577 Semigroup, elementary 579 580 Semigroup, free 6 Semigroup, free commutative 7 577 Semigroup, nil See nilsemigroup Semigroup, subelementary 579 580 Semilattice 539—541 542 Semilattice, lower 539 Semilattice, upper 540 Separate the elements 575 Sequence, addible 131 268 Sequence, Cauchy 233 243—245 247—248 268 462 Sequence, connected 478 484 485 Sequence, empty 6 Sequence, exact 393 393—397 465 604 Sequence, exact cohomology 468 504 Sequence, exact homology 465 Sequence, Hom-Ext 491 Sequence, Ker — Coker 467 471 Sequence, left exact 394 419 420 Sequence, Mayer — Vietoris 470 Sequence, null 393 Sequence, right exact 394 420 Sequence, short exact 394 Sequence, split exact 395 604 Sequence, summable 130 Sequence, Tor 494 Sequence, transfinite 635 Series See also Laurent series. See also power series Series of submodules 348 Series subnormal 71 Series, central 89 639 Series, commutator 84 Series, composition 73 74 Series, normal See normal series Set See also algebraic set. See also ordered set. See also preordered set Set, countable 641 642 Set, finite 641 Set, infinite 641 Set, quasiordered See preordered set Set, quotient 561 Set, transitive 631 Set, underlying 3 8 Set, zero 307 Sets 583 Sign of permutation 60 simplex 463 Simplex, singular 463 Simplex, standard 463 Skeleton 590 Skolem — Noether theorem 536 SL 77 Solution set condition 610 Space, affine 307 Space, projective 79 307 Space, Stone 555 556 557 Spectrum 301 Spencer, M. viii Stabilizer 55 Steinitz, E. 155 Stickelberger, L. 45 Stone space 556 557 558 Stone, M. 539 555 556 Stone’s theorem 555; 556 Structure, cycle 61 Structure, module 315 316 Subalgebra 516 560 Subalgebra, generated by a subset 519 564 Subalgebra, graded 517 Subdirect product 574 574—580 Subfield 155 156 157 Subfield, generated by subset 158 Subgroup 12 12—18 Subgroup of 14 Subgroup of quotient group 21 Subgroup, characteristic 58 Subgroup, commutator 83 Subgroup, cyclic 14 Subgroup, Frattini 17 Subgroup, fully invariant 88 91 Subgroup, generated by subset 13 Subgroup, Hall 86 86—88 Subgroup, maximal 17 92 Subgroup, normal 19 Subgroup, subnormal 71 Subgroup, Sylow 65 65—67 85 91 Sublattice 542 Sublattice, Boolean 555 Submodule 278 318 Submodule of free module 336 337 411 Submodule of quotient module 322 Submodule, anticommutative 524 Submodule, cyclic 318 Submodule, essential 329 408 Submodule, finitely generated 278 318 Submodule, generated by monomials 351 Submodule, generated by subset 278 318 Submodule, graded 517 Submodule, large 408 Submodule, membership problem 351 Submodule, pure 448 Submodule, syzygy 354 Subring 109 110 Subring of field 155 Subring of quotient ring 114 Subring of ring extension 278 Subring, generated by subset 112 158 Subsemigroup 578 Subset, algebraically dependent 182 Subset, algebraically independent 182 Subset, cofinal 429 Subset, cofinite 557 Subset, dense 372 Subset, linearly independent 330 Subset, multiplicative 281 Subset, proper multiplicative 281 Substitution in polynomials 122 125 Substitution in power series 132 Subtraction 106 Successor 633 634 SUM See also direct sum Sum of cardinal numbers 642 644 Sum of elements 4 Sum of ideals 111 Sum of ordinal numbers 635 Sum of power series 131 Sum of submodules 319 Sum of subsets 4 Sum, direct 328 Sum, infinite 107 Summand of free module 402 Summand, direct 328 402 404 451 Support of permutation 60 Supremum See least upper bound Surgery 160 Sylow theorems 64—67 Sylow, L. 64 65 System, direct 423 System, inverse 430 Syzygy 354 471 507—508 T, a group 36 69 table 4 Table, Light’s 5 Tensor product 435 434—448 Tensor product of algebras 527 527—530 594 Tensor product of bimodules 438 438—441 444 Tensor product of elements 434 436 Tensor product of exact sequences 445 446 Tensor product of fields 530—534 Tensor product of free modules 439 Tensor product of graded algebras 530 Tensor product of modules 435 444 449—451 Tensor product of vector spaces 434 Term 148 Term, leading 149 351 terminate 624 626 145 292 296 346 347 Thompson, J.G. 83 Topology on power series ring 132 Topology, algebraic 8 18 20 37 41 43 83 463 464 465 470 497 500 Topology, compact-open 372 Topology, finite 201 203 Topology, Krull 202 201—204 272 462 Topology, profinite 27 Topology, Stone 555 Topology, Zariski 309 310 TOPS 617 Tor 493 493—496 Torsion 339 Tower of field extensions 158 Tower, property 160 164 170 172 175 183 189 195 217 281 Trace of element 215 215—219 Trace of linear transformation 215 Transcendence base 183 Transcendence base, separating 187 Transformation 2 Transformation, chain 464 Transformation, diagonalizable 345 Transformation, linear 320 342—346 Transformation, natural 417 587 Transformation, nilpotent 346 Transformation, projective 79 Transformation, rational 312 Transporter 273 274 Transposition 58 Trihomomorphism 444 Triple 613 613—620 Trisection of angle 226 Type of universal algebra 560 Union of congruences 562 Union of ideals 111 Union of subalgebras 560 Union of subgroups 15 Union of submodules 318 Union of subrings 112 Union, directed 568 Unique factorization domain 141 141—145 283 304 Unit of polynomial ring 121 127 Unit of power series ring 131 Unit of ring 109 Universal algebra 560 559—580 Universal algebra of type T 560 Universal algebra, free 569 573 622 Universal algebra, quotient 561 Universal algebra, subdirectly irreducible 575 Universal algebra, word 565 564—567 Universal coefficient theorem 497 499 Universal property 610 612 Universal property of 108 Universal property of 233 Universal property of 114 Universal property of category of T -algebras 616 Universal property of coequalizer 594 Universal property of cokernel 393 394 601 Universal property of colimit 594 Universal property of completion 244 459 Universal property of coproduct 594 Universal property of derived group 84 Universal property of direct limit 425 Universal property of direct product 47 325 Universal property of direct sum 326 Universal property of exterior algebra 524 Universal property of exterior power 525 Universal property of field of fractions 117 Universal property of free category 591 Universal property of free group 30 Universal property of free module 331 Universal property of free product 40 Universal property of free product with amalgamation 42 Universal property of free universal algebra 569 Universal property of group algebra 382 Universal property of initial object 609 Universal property of inverse limit 431 Universal property of kernel 393 394 601 Universal property of left derived functor 481 Universal property of left exact sequence 394 Universal property of limit 592 Universal property of localization 285 Universal property of polynomial rings 123 128 Universal property of power series rings 269 Universal property of presentation 33 Universal property of product 592 Universal property of pullback 397 593 Universal property of pushout 399 595 Universal property of quotient algebra 517 562 Universal property of quotient group 23 Universal property of quotient module 322 Universal property of quotient ring 114 Universal property of right derived functor 484 485 Universal property of right exact sequence 394 Universal property of ring of fractions 285 Universal property of simple field extension 163 Universal property of symmetric algebra 521 Universal property of symmetric power 522 Universal property of tensor algebra 520 Universal property of tensor product 434 436 529 Universal property of terminal object 609 Universal property of word algebra 565 Universe 581 Uzkov, A.I. 285 Valuation 251 251—261 Valuation ring 252 253 254 256 288 Valuation ring of field 253 Valuation ring, discrete 254 255 Valuation, discrete 254 Valuation, domain See valuation ring Valuation, induced by valuation ring 253 Valuation, real 239 Value, absolute See absolute value Van der Waerden, B. 155 Variety of type T 567 567—573 575 621—624 Variety, algebraic 300 309 Variety, generated by a class 571 Vector space 315 334 334—336 Vector space, normed 247 Vertex 583 Wedderburn, J. 209 359 Wedderburn’s theorem 209 534 Weil, A. 309 Well defined 23 Whitehead, A. 559 Word 6 27 38 Word, reduced 27 38 41 Yoneda’s Lemma 590 Zariski, O. 309 Zassenhaus, H. 72 102 Zassenhaus’s lemma 72 Zen Buddhism 2 Zermelo, E. 628 629 Zero element of ring 106 Zero element of semigroup 577 Zorn, M. 628 Zorn’s Lemma 628 111 636
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