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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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Предметный указатель
Modules See also module Modules, injectively equivalent 510 Modules, isomorphic 320 Modules, projectively equivalent 507 Monad See triple Monoid 3 614 Monoid of endomorphisms 20 Monoid, commutative 3 Monoid, free 6 120 Monoid, free commutative 7 126 Monomial 6 125 Monomial, leading 149 351 Monomorphism 19 107 584 Monomorphism of modules 320 393 Monomorphism, essential 409 Monomorphism, split 395 404 Moore, E. 543 Moore, J.C. 613 Morphism 582. See also homomorphism Morphism of algebraic varieties 312 Morphism of diagrams 591 Morphism of T -algebras 614 Morphism, codiagonal 601 Morphism, diagonal 601 Morphism, identity 582 Morphism, natural 587 Morphism, zero 600 Multihomomorphism 443 Multilinear mapping 443 Multilinear mapping, alternating 524 525 Multilinear mapping, symmetric 522 Multiple, integer 4 11 106 114—115 Multiple, least common 135 136 142 Multiplication 2 Multiplicity of root 122 125 Nagata, M. 376 Nakayama, I. 376 Nakayama’s Lemma 302 303 376 Nielsen, J. 27 Nilradical 274 Nilsemigroup 577 Nine lemma 395 397 470 Node 583 Noether — Lasker theorem 276 Noether, E. vii 105 146 273 295 529 535 534 Noether’s theorem 535 Norm of element 215 215—219 Norm on vector space 247 Normal series 70 72 Normal series, ascending central 90 639 Normal series, central 89 Normal series, descending central 89 Normal series, equivalent 71 348 Normalization 283 normalizer 65 67 Notation, additive 2 4 11 13 Notation, multiplicative 2 Nullstellensatz 308 Number of elements 639 641 Number, algebraic 236 Number, cardinal See cardinal number Number, ordinal See ordinal number Number, p-adic 245 246 Object 582 Object, initial 609 612 Object, terminal 609 612 Object, zero 600 Operation, associative 3 Operation, binary 1 559 Operation, commutative 3 Operation, componentwise 43 Operation, constant 2 559 Operation, idempotent 540 Operation, n -ary 2 559 Operation, order preserving 540 Operation, partial 2 559 Operation, unary 2 559 Opposite of element 8 Opposite of sum 11 Orbit 55 ord 632 Order of center 57 Order of conjugacy class 56 Order of element of a group 24 Order of group 16 Order of orbit 55 Order of permutation 62 Order of polynomial 239 Order of power series 130 Order of quotient group 21 Order of subgroup 16 17 Order relation 625 631 Order relation, opposite 626 Order relation, partial 625 Order relation, total 625 Order, degree lexicographic 148 Order, degree reverse lexicographic 148 Order, lexicographic 148 Order, monomial 148 351 Order, term 148 Ordered set See also partially ordered set. See also preordered set Ordered set, totally 625 423 Ordered set, well 629 633 Ordinal number 631 631—639 Ordinal number, limit 634 Ordinal number, successor 633 634 Origin 583 Orthogonality of characters 388 389 Ostrowski, A. 241 247 Ostrowski’s theorem 249 Partially ordered set 625 423. Partially ordered set, dual 540 Partially ordered set, Noetherian 626 Partially ordered set, opposite 627 540 Partition 16 45 55 62 Path 583 Path, empty 583 Peirce, B. 104 515 Permutation 9 58—63 Permutation, conjugate 62 Permutation, disjoint 60 Permutation, even 59 Permutation, fixed point of 60 Permutation, odd 59 Permutation, sign of 60 Permutation, support of 60 Place 255 Polygon, regular 9 226 Polynomial 120 126 119—130. Polynomial equation vii 1 191 Polynomial equation of degree 2 vii 1 191 205 Polynomial equation of degree 3 191 205—207 Polynomial equation of degree 4 191 207—208 Polynomial equation of degree 5 191 Polynomial equation, general 223 223—225 Polynomial in one variable 120 119—125 Polynomial in several variables 126 125—130 Polynomial of degree 2 205 Polynomial of degree 3 205—207 209 210 Polynomial of degree 4 208—209 210 Polynomial, characteristic 216 345 Polynomial, constant 120 126 Polynomial, cyclotomic 211 211—215 Polynomial, elementary symmetric 177 224 Polynomial, general 223 Polynomial, homogeneous 129 Polynomial, irreducible 136—138 143—145 233 Polynomial, minimal 343 345 Polynomial, monic 121 Polynomial, primitive 142 258 Polynomial, separable 169 Polynomial, splitting 191 Polynomial, symmetric 224 pos 616 Power 3 10 642 Power series 130 130—133 245 254 267—269 Power, exterior 525 Power, symbolic 298 Power, symmetric 523 Power, tensor 519 Preimage See inverse image Preordered set 423 428 583 585 612 616. Preordered set, directed 423 Presentation 34 31—37 Presentation, projective 471 Preserve colimits 598 608 Preserve limits 597 608 621 Preston, G.B. 5 Primitive Element Theorem 171 Principal ideal domain 133 133—138 254 293 294 295 336—342 403 405 411 497 PRODUCT 2 592 595. Product of cardinal numbers 642 643 644 Product of elements 2 Product of ideals 112 269 Product of left ideal and submodule 319 320 Product of left ideals 319 Product of morphisms 582 598 Product of ordinal numbers 635 Product of subsets 4 Product, balanced 435 443 Product, empty 2 Product, semidirect 93 92—94 102 Product, torsion See Tor Projection from direct product 44 325 568 Projection from group extension 95 Projection from product 592 Projection from semidirect product 93 Projection to quotient algebra 561 Projection to quotient group 20 Projection to quotient module 321 Projection to quotient ring 113 Projection to quotient set 561 PSL 79 Pullback 593 604 Pullback of modules 397 398 400 423 429 433 593 Pushout 595 Pushout of modules 399 398—401 423 429 448 Q, quaternion group 35 69 Quadrature of circle 229 Quotient of ideals 273 Quotient, group 20 Quotient, module 321—322 Quotient, ring 113 Quotient, universal algebra 562 R((X )) 131 R(X ) 124 R-Algs 584 RAD 274 Radical 375 Radical of ideal 274 Radical, Jacobson 375 374—377 Radical, nil 274 RANGE 19 113 321 Rank of module 334 335 Rational fraction 124 129 139—141 Rational fraction, symmetric 224 Recursion 637 638 Redei, L. 148 580 Redei’s theorem 148 580 Reduction 27 29 38 39 Refinement of normal series 71 348 Relation See also order relation Relation of type T 565 Relation, defining 33 Relation, equivalence 561 Relation, group 27 32 Remak, R. 48 Representation of group 380 382 380—392 Representation of group, complex 389 389—392 Representation of group, equivalent 380 382 Representation of group, irreducible 381 384 Representation of group, regular 380 Representation of group, trivial 380 Resolution 471—478 Resolution, bar 505 502—505 Resolution, flat 496 Resolution, free 471 504 Resolution, injective 476 476—478 491 508 Resolution, projective 471 471—476 491 494 507 508 Resultant 176 176—178 Ring 105 105—154 273—318 366—379. Ring extension 277 277—284 515 Ring extension, finitely generated 278 288 Ring extension, integral 280 280—282 287 288 Ring of endomorphisms 316 332 360 364 370—374 Ring of fractions 285 285—290 Ring of matrices 106 332 360—362 364 370 371 377 515 Ring of polynomials 119—130 147 142—144 276 305—306 308 309 510—514 515 517 522 577 Ring with identity 105 Ring with unity 104 Ring, affine 311 Ring, associative 106 Ring, blown-up 457 Ring, boolean 554 Ring, change of 440 441 461 Ring, commutative 106 115—119 269—314 318 Ring, complete 267 267—272 Ring, coordinate 310 310—314 Ring, division 116 209 334 336 360 384 538 Ring, euclidean 138 Ring, free commutative 129 Ring, group 120 382; Ring, isomorphic 107 Ring, Jacobson semisimple 378 377—379 Ring, left Artinian 348 349 377—379 Ring, left hereditary 411 411—414 497 499 510 Ring, left Noetherian 347 349 407 429 Ring, left primitive 372 372—374 377 Ring, local 287 403 Ring, Noetherian 146 146—148 287 296 Ring, nonassociative 106 Ring, opposite 317 332 361 442 Ring, reduced 532 Ring, regular 109 370 379 Ring, right Artinian 348 Ring, right Noetherian 347 Ring, right primitive 372 Ring, semigroup 120 124 Ring, semiprimitive 378 Ring, semisimple 359 366 366—370 377 383 402 404 510 Ring, simple 360 Ring, valuation See valuation ring Ring, von Neumann regular 109 370 379 Rings 584 Root 122. See also root of unity Root of unity 157 Root of unity, primitive 157 211 Root, multiple 122 Root, simple 122 123 Russell’s paradox 631 R[X ] 120 R[[X ]] 130 Schanuel’s Lemma 507 Schering, E. 45 Schmidt, O. 48 Schreier, O. 41 71 97 217 231 236 Schreier’s theorem 71 348; Schreyer, F. 355 Schreyer’s theorem 355 Schur — Zassenhaus theorem 102
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