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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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Cross section of group extension 95 Curve, algebraic 271 307 CYCLE 60 464 Cylinder, mapping 470 dc.c See descending chain condition Decomposition, subdirect 575 578 Dedekind domain 293 295—297 413—414 497 Dedekind, R. 104 155 273 290 539 Degree of element 162 Degree of field extension 160 Degree of group representation 380 Degree of monomial 127 Degree of polynomial 121 127 Degree, residual class 254 254—257 Degree, separability 170 Degree, transcendence 184 311 Derivative 123 Destination 583 Determinant 526 527 diag 591 Diagram 590 Diagram, commutative 591 Diagram, constant 592 Dimension of algebraic variety 309 312 Dimension of group representation 380 Dimension of vector space 336 Dimension, global 510 511 510—514 Dimension, injective 509 Dimension, Krull 305 306 310 Dimension, projective 509 507—510 Direct limit 424 423—429 433 Direct limit of complexes 470 Direct limit of exact sequences 428 Direct limit of modules 424 427 447 451 453 455 497 Direct limit of sets 424 425 Direct limit of universal algebras 573 624 Direct product of bimodules 423 Direct product of Boolean lattices 557 Direct product of complexes 470 Direct product of groups 43 48 43—49 592 Direct product of homomorphisms 325 Direct product of injective modules 404 Direct product of modules 325 328 420 491 592 Direct product of projective modules 403 Direct product of rings 364—366 375 Direct product of universal algebras 568 Direct sum of complexes 470 Direct sum of group representations 380 Direct sum of groups 44 49 Direct sum of homomorphisms 326 Direct sum of injective modules 407 Direct sum of modules 325 325—329 402 421 429 433 446 451 491 494 495 508 594 Direct sum of projective modules 402 Direct sum, external 325 Direct sum, internal 327 Dirichlet, G. 188 214 Dirichlet’s Theorem 214 Discriminant 179 179—181 206 Distributivity 105 315 548 567 Division, polynomial 121 149 Divisor, greatest common 135 136 142 Domain 116 115—119 582 630. Domain of binary relation 631 Domain, integral 116 Domain, integrally closed 283 284 287 295 296 Domain, normal 283 Domain, valuation See valuation ring Doohickey 416 Duality principle 540 541 543 546 549 553 585 Duplication of cube 226 Dyck, W. 27 31 33 Dyck’s theorem 33 EDGE 583 Eigenspace 345 Eigenvalue 345 Eilenberg, S. 401 403 463 500 613 Eisenstein, G. 144 Eisenstein’s Criterion 144 145 262 Element See also elements Element, algebraic 161 162 280 Element, cancellative 578 Element, central 382 516 Element, greatest 627 543 Element, idempotent 370 Element, identity See identity element Element, integral 279 280 281 Element, irreducible 134 142 550 Element, least 629 543 Element, left quasiregular 377 Element, maximal 625 111 145 Element, minimal 627 Element, nilpotent 112 376 377 577 Element, prime 134 142 Element, primitive 161 Element, purely inseparable 174 Element, quasiregular 377 Element, radical 218 Element, representative 133 Element, separable 171 Element, torsion 339 Element, torsion-free 339 Element, transcendental 161 Element, unique maximal 627 Element, zero See zero element Elementary linear transformation 77 Elementary matrix 77 Elements See also element Elements, algebraically dependent 182 Elements, algebraically independent 182 Elements, associate 133 Endomorphism of abelian group 106 Endomorphism of group 20 Endomorphism of module 320 Endomorphism of vector space 106 Endomorphism, nilpotent 51 Endomorphism, normal 50 Endomorphism, projection 52 Envelope, injective See hull injective Epimorphism 19 107 584 Epimorphism of modules 320 393 Epimorphism, split 395 402 Equalizer 593 595 Equipotence 640 Equivalence of categories 588 609 Equivalence of group extensions 95 98 Erlanger Programme 1 Euclid 138 Evaluation of polynomials 122 128 Evaluation of rational fractions 124 129 Exchange property 50 182 335 expansion 286 287 Exponentiation of cardinals 642 644 Ext 490 Extension of absolute values 247—261 Extension of fields See field extension Extension of groups See group extension Extension of rings See ring extension Extension of valuations 256—261 Extension, essential 409 408—410 Factor of normal series 71 348 Factor set 96 Factor, simple 74 Factorization theorem for algebras 517 Factorization theorem for groups 23 Factorization theorem for modules 322 Factorization theorem for rings 114 Factorization theorem for universal algebras 562 Family, algebraically dependent 182 Family, algebraically independent 182 Family, directed 15 423 425 568 Family, linearly independent 330 Feit and Thompson theorem 83 Feit, W. 83 Fermat prime 229 Field 116 155—268 569. Field extension 159 159—230 530—534 Field extension, algebraic 164 164—230 Field extension, conjugate 194 199 Field extension, cyclic 219 218—220 Field extension, finite 160 164 297 Field extension, finitely generated 161 Field extension, Galois 197 197—225 297—300 Field extension, infinite 160 Field extension, infinite Galois 200—204 Field extension, linearly disjoint 185 186 532 Field extension, normal 192 191—197 199 225 Field extension, purely inseparable 173 172—175 192 Field extension, purely transcendental 181 Field extension, quadratic 283 Field extension, radical 221 Field extension, separable 171 169—172 189 184—190 195 532 Field extension, simple 161 162 170 Field extension, solvable by radicals 221 221—225 Field extension, totally transcendental 181 Field extension, transcendental 164 181—190 Field of fractions 118 119 285 Field of rational fractions 124 128 531 Field, algebraically closed 166 Field, Archimedean 232 233 Field, complete 243 249 259 264 Field, cyclotomic 212 Field, finite 192—193 Field, fixed 198 202 Field, formally real 234 234—239 Field, Galois 193 Field, ordered 231 231—239 Field, perfect 196 197 237 238 Field, quotient See field of fractions Field, real closed 235 235—239 Field, residue class 258 258—261 Field, skew 334 Field, splitting 191 192 191—193 Filter 462 Filtration on module 456 456—458 Filtration on ring 266 266—272 Filtration, 456 Filtration, 266 456 Filtration, 457 458 Five lemma 394 Fixed point 60 FRACTION 118 285. Fraction, partial 139 Fraction, polynomial free 139 Fraction, reduced 139 Fractional ideal 290 291 Fractional ideal, finitely generated 291 Fractional ideal, invertible 291 413 Free product of groups 40 37—42 594 Free product of groups with amalgamation 41 42 584 595 Freyd, P. 609 Frobenius, G. 45 515 538 Frobenius’s Theorem 538 Func 587 Function, choice 628 Function, class 387 582 Function, coordinate 106 310 Function, Euler’s 46—47 207 Function, polynomial 311 Function, rational 129 311 314 functor 416 586 586—590 Functor, 437 438 445—448 607 Functor, additive 417 603 Functor, adjoint 606 604—612 Functor, colimit 599 606 Functor, completion 459 460 Functor, contravariant 416 588 Functor, covariant 416 586 Functor, derived 478—487 Functor, direct limit 427—429 Functor, dual 448 Functor, exact 419 420 Functor, Ext 488—493 507 Functor, forgetful 586 596 604 607 611 621 622 Functor, free group 586 604 Functor, free module 605 613 Functor, hom 417 418—423 589 597 599 Functor, homology 464 Functor, identity 587 Functor, inverse limit 432—434 Functor, left adjoint 606 622 Functor, left derived 479 479—484 486 Functor, left exact 419 Functor, limit 598 599 606 Functor, representable 612 Functor, right adjoint 606 Functor, right derived 484 485 486 Functor, right exact 445 Functor, Tor 493 493—496 Functor, tripleable 616 616—621 623 Fundamental theorem of algebra 137 Fundamental Theorem of Finitely Generated Abelian Groups 44 339 Fundamental Theorem of Galois Theory 198 203 g.l.b See greatest lower bound Galois connection 200 544 545 Galois group 197 204 197—225 224 299—300 Galois group of extension of 214 Galois group of polynomial 204 204—211 Galois, E. 1 191 192 Garibaldi, S. viii Gauss integer 109 Gauss, G. 105 137 142 229 262 Gauss’s Lemma 143 262 GCD 135 Geometry, algebraic 271 273 275 276 307—314 GL 76 Goedel, K. 628 Going up 282 Gorenstein, D. 74 Graph 583 Graph, directed 583 Graph, discrete 592 Graph, finite 598 Graph, square 583 Graph, triangle 583 Grassmann, H. 523 Grell, H. 285 Grillet, P.A. 579 Grillet’s theorem 579 Groebner basis of ideal 150 148—154 Groebner basis of module 352 350—358 Groebner, W. 148 Group 8 1—104. Group action See group action Group action, left 54 55 Group action, right 54 Group action, trivial 501 Group cohomology 100 464 468 500—507 Group extension 95 95—104 Group extension, equivalent 95 98 Group extension, split 99 Group generator 33 Group homology 463 464 Group of automorphisms 20 55 Group of finite length 49 Group of homomorphisms 415—423 Group of isometries 9 Group of rotations and symmetries 9 Group, alternating 36 60 74 Group, amalgam 41 Group, classical 76—83
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