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Hungerford T.W. — Algebra
Hungerford T.W. — Algebra

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Название: Algebra

Автор: Hungerford T.W.

Аннотация:

Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents. The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises. The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 502

Добавлена в каталог: 02.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Aut_{K}F$      243
$Hom_{R}(A,B)$      174 199ff
$\phi$-invariant subspace      356
(Greatest) lower bound      14
A.C.C.      see "Ascending chain condition"
Abel's theorem      308
Abelian extension field      292
Abelian field extension      292
Abelian group      24 70ff 76ff
Abelian group defined by generators and relations      343ff
Action of group on set      88ff
Additive notation for groups      25 29 38 70
Adjoining a root      236
Adjoint Associativity      214
Adjoint functor      477ff
Adjoint pair of functors      477ff
Affine variety      409
Aitin, E.      vi 251 252 288
Algebra module(s)      451
Algebra(s)      226ff 450ff
Algebra(s) ideal      228
Algebraic algebra      453
Algebraic closure      259ff
Algebraic dependence      311ff
Algebraic element      233 453
Algebraic extension field      233ff
Algebraic field extension      233ff
Algebraic independence      311ff
Algebraic number      242
Algebraic set      409
Algebraically (in)dependent      311ff
Algebraically closed field      258
Algorithm multilinear function      349
Alternating group      49
Annihilator      206 388 417
Anti-isomorphism      330
Antisymmetric relation      13
Artinian module      372ff
Artinian rings      372ff 419ff 421 435ff
Ascending central series      100
Ascending chain condition      83 372ff
Associate      135
Associated prime ideal      380 387
Associative binary operation      24
Automorphism      30 119
Automorphism of a group      30 90
Axiom of Choice      13
Axiom of class formation      2
Axiom of extensionality      2
Axiom of pair formation      6
Baer lower radical      444ff
Basis      71 181
Bijective function      5
Bilinear function(s)      211 349
Bilinear map      211 349
Bimodule      202
Binary operation      24
Binomial coefficient      118
Binomial theorem      118
Boolean ring      120
Cancellation      24 116
Canonical bilinear map      211
Canonical epimorphism      43 125 172
Canonical forms      337
Canonical injection      60 130 173
Canonical injections      60 130 173
Canonical middle linear map      209
Canonical projection      8 59 130 173
Cardan's formulas      310
cardinal number      16ff
Cardinal number(s) inequalities      17
Cardinality      16
Cartesian product      6 7ff
Category      52ff 464ff
Category, concrete      55
Cauchy's theorem      93
Cayley — Hamilton theorem      367 369
Cayley's theorem      90
Center of a group      34 91
Center of a ring      122
Central idempotents      135
Central simple division algebra      456
centralizer      89
Chain      13
Chain conditions      83ff 372ff
Chain conditions on submodule(s)      372ff
Char R      119
Characteristic of a ring      119
Characteristic polynomial      366ff
Characteristic polynomial of a linear transformation      366ff
Characteristic polynomial of an endomorphism(s)      366ff
Characteristic polynomials of matrices      366ff
Characteristic space      368
Characteristic subgroups      103
Characteristic values      367
Characteristic vectors      367
Chinese remainder theorem      131
Choice function      15
class      2ff
Class equation      90 91
Classical adjoint      353
Classical adjoint matrix      353
Classification of finite groups      96ff
Closed intermediate field      247
Closed object      410
Closed subgroups      247
Closed under a binary operation      31
Codomain      3
Coefficients of Polynomial(s)      150
Coequalizer      482
Cofactor      352
Cohen, I.S.      388
Coimage      176
Cokernel      176
Cokernel of a morphism      483
Column rank      336 339
Column space      336
Column vector      333
Commutative binary operation      24
Commutative diagram      4
Commutative group      24
Commutative ring      115
Commutator      102
Commutator subgroup      102
Companion matrices      358
Companion matrix      358
Comparable elements      13
Complement      3
Complete direct sum      59
Complete lattice      15
Complete ring of quotients      144
Complete set of coset representatives      39
Completely reducible module      437
Composite function      4
Composite functor      468
Composite morphism      52
Composite subfield      233
Composition series      108 375
Concrete category      55
Congruence modulo a subgroup      37
Congruence modulo m      12
Congruence relation      27
Conjugacy class      89
Conjugate elements or subgroups      89
Conjugation      88
Constant polynomial      150
Constant term      150 154
Constructible number      239
Content of a polynomial      162
Continuum Hypothesis      17
Contraction of an ideal      146 398
Contravariant functor      466
Contravariant horn functor      466
Conway, C.T.      xiii
Coordinate ring      413
Coproduct      54ff
Coset      38ff
Couniversal object      57
Covariant functor      465
Covariant horn functor      465
Cramer's rule      354
Cycles      46
Cyclic extension field      289ff 292
Cyclic field extension      289ff
Cyclic group      32 35ff
Cyclic module      171
Cyclic subgroup(s)      32
Cyclic submodule(s)      171
Cyclic subspace      356
Cyclotomic extension      297ff
Cyclotomic extension field      297ff
Cyclotomic polynomial      166 298
D.C.C.      see "Descending chain condition"
Decomposition of a linear transformation      355ff
Dedekind domain      401ff
Degree of a field element      234
Degree of a monomial      157
Degree of a polynomial      157 158
Degree of inseparability      285ff
DeMorgan's laws      3
Dense ring      418
Dense ring of endomorphism(s)      418
Density theorem      420
Denumerable set      16
Derivative      161
Derived subgroup      102
Descending chain condition      83 372ff
Determinant      351ff
Determinant of an endomorphism      354
Determinants of matrices      351ff
Diagonal matrix      328
Difference cokernel      482
Difference kernel      482
Dihedral group      50
DIMENSION      185ff
Direct factor      63
Direct product      26 59ff 130 131 173
Direct product of group(s)      26 59ff
Direct product of module(s)      173
Direct product of ring(s)      130 131
Direct sum      60 62ff 173 175
Direct sum of group(s)      60 62
Direct sum of matrices      360
Direct sum of module(s)      173 175
Direct summand      63 437
Discrete valuation ring      404
Discriminant      270
Discriminant of Polynomial(s)      270
Disjoint cycles      47
Disjoint permutations      47
Disjoint sets      3
Disjoint union      58
Divisible abelian group      195ff
Divisible group      195ff
Division algebras      227 456ff
Division algorithm      11 158
Division ring      116
Division ring of real quaternions      117 461
Domain of a function      3
Double dual      205
Dual basis      204
Dual category      466
Dual map      204
Dual module      203ff
Dual statement      54
Eigenspace      368
Eigenvalues      367ff
Eigenvalues of a linear transformation      367
Eigenvalues of matrices      368
Eigenvectors      367ff
Eigenvectors of a linear transformation      367
Eigenvectors of matrices      368
Eisenstein's criterion      164
Elementary column operation      338
Elementary divisors      80 225 357 361
Elementary divisors of a linear transformation      357
Elementary divisors of matrices      361
Elementary Jordan matrices      359
Elementary Jordan matrix      359
Elementary matrices      338
Elementary row operation      338
Elementary row or column operation      338
Elementary symmetric functions      252
Elementary transformation matrix      338
Embedded prime      384
Embedded prime ideal      384
Embedding      119
Empty set      3
Empty word      64
End A      116
Endomorphism(s) of a group      30
Endomorphism(s) ring      116 179 415
Epic morphism      480
Epimorphism      30 118 170
Epimorphism in a category      480
Equality      2
Equalizer      482
Equipollent sets      15
Equivalence class      6
Equivalence in a category      53
Equivalence relation      6
Equivalent matrices      332 335ff
Equivalent series      109 375
Euclidean algorithm      141
Euclidean Domain      139
Euclidean ring      139
Euler function      297
Evaluation homomorphism      153
Even permutation      48
Exact sequence      175ff
Exact sequence of module(s)      175ff
Expansion of a determinant along a row      353
Exponentiation in a group      28
Exponentiation of cardinal numbers      22
Extendible automorphism      251 260
Extension field      231ff
Extension of an ideal      145
Extension ring      394ff
External direct product      130
External direct sum      60 173
External weak direct product      60
Factor group      42ff
Factorization in commutative rings      135ff
Factorization in polynomial rings      157ff
Factors of a series      107 375
Faithful module      418
Field      116 230ff
Field extension      231ff
Field of rational functions      233
Finite dimensional algebra      227
Finite dimensional field extension      231
Finite dimensional vector space      186
Finite division ring      462
Finite field      278ff 462
Finite group      24 92ff 96ff
Finite set      16
Finitely generated abelian group      76ff
Finitely generated abelian groups      76ff 343ff
Finitely generated extension field      231 232
Finitely generated group      32
1 2 3
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