Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Hungerford T.W. — Algebra
Hungerford T.W. — Algebra



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


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
blank
Предметный указатель
Finitely generated ideal      123
Finitely generated module      171
Finitely generated submodule(s)      171
First isomorphism theorem      44 126 172
Fitting's lemma      84
Five lemma      180
Fixed field      245
Forgetful functor      466
Formal derivative      161
Formal power series      154ff
Four group      29
Fractional ideal      401
Free Abelian group      71ff
Free group      65ff
Free module      181ff 188
Free object functor      479
Free object in a category      55ff
Free product      68
Free product of group(s)      68
Freshman's dream      121
Frobenius theorem      461
Fully invariant subgroup      103
Function(s)      3ff
functor      465ff
Fundamental theorem of algebra      266
Fundamental Theorem of Arithmetic      12
Fundamental Theorem of Galois Theory      245ff 263
g.l.b.      14
Galois correspondence      246
Galois extension      245
Galois extension field      245
Galois fields      278ff
Galois group of a polynomial      269ff
Galois group(s) of a polynomial      269ff
Galois groups      243
Galois theory      230ff
Gauss lemma      16
Gaussian integers      139
General equation of degree n      308ff
General polynomial of degree n      308
Generalized associative law      28
Generalized commutative law      28
Generalized fundamental theorem of Galois Theory      263
Generalized multiplicative system      449
Generators and relations      67ff 343ff
Generators of a group      32
Generators of a module      171
Generators of an ideal      123
Going-up Theorem      399
Goldie ring      447ff
Goldie's Theorem      448
Goldmann ring      400
Graph      6
Graph of a function(s)      6
Greatest common divisor      11 140
Greatest lower bound      14
Group algebra(s)      227
Group ring(s)      117
Group(s)      24ff
Group(s) defined by generators and relations      67 343ff
Group(s) of integers modulo m      27
Group(s) of rationals modulo one      27
Group(s) of small order      98
Group(s) of symmetries of the square      26
Hall's theorem      104
Halmos, P.      ix
Hilbert basis theorem      391
Hilbert nullstellensatz      409ff 412
Hilbert's theorem      90 292
Hom functor      465 466
Homogeneous of degree k      158
Homogeneous system of equations      346
Homomorphism of algebras      228
Homomorphism of groups      30ff 43ff
Homomorphism of modules      170ff 199ff
Homomorphism of rings      118
Hopkin's Theorem      443
Ideal(s)      122ff
Ideal(s) generated by a set      123
Idempotent element      135 437
Identity      24 115
Identity element of a group(s)      24
Identity function      4
Identity functor      465
Identity matrix      328
Image of a function      4
Image of a homomorphism      31 119 170
Image of a set      4
Immediate predecessor      14
Immediate successor      15
Inclusion map      4
Indecomposable group      83
Independent set of ideals      446
Indeterminate      150 152
Index of a subgroup      38
Induced homomorphism      199 209
Induced homomorphism on the tensor product      209
Infinite set      16
Initial object      57
Injective function      4
Injective module      193ff
Inner automorphism      91 459
Inseparable degree      285ff
Integers      9ff
Integers modulo m      27 116
Integral closure      397
Integral domain      116
Integral element      395
Integral extension      395
Integral ring extension      395
Integrally closed ring      397
Intermediate field      231
Intermediate Value Theorem      167
Internal direct product      131
Internal direct sum      62 175
Internal weak direct product      62
Intersection      3
Invariant dimension property      185
Invariant factors      80 225 357 361
Invariant factors of a linear transformation      357
Invariant factors of matrices      361
Invariant subspace      356
Inverse      24 116
Inverse image      4 31
Inverse of a matrix      331
Inverses in group(s)      24
Invertible element      116
Invertible fractional ideal      401
Invertible ideal(s)      401
Invertible matrices      331
Invertible matrix      331
Irreducible element      136
Irreducible module      416
Irreducible polynomial      161 234
Irreducible variety      413
Irredundant primary decomposition      381
Isolated prime ideal      384
Isomorphic group(s)      30
Isomorphism      30 118 170
Isomorphism theorems      44 125ff 172ff
Isomorphism theorems for module(s)      172ff
Isotropy group      89
Jacobson density theorem      420
Jacobson radical      426ff
Jacobson semisimple      429
Join of groups      33
Join of subgroup(s)      33
Jordan canonical form      361
Jordan — Hoelder theorem      111 375
k-algebra      see "Algebra"
K-automorphism      243
K-homomorphism      243
Kaplansky, I.      vi 251 391 432
Kernel      31 119 170
Kernel of a homomorphism      31 119 170
Kernel of a morphism      483
Klein Four group      29
Kronecker delta      204
Kronecker's method      167
Krull intersection theorem      389
Krull — Schmidt theorem      86
l.u.b.      14
Lagrange's interpolation formula      166
Lagrange's theorem      39
Lattice      14
Law of Well Ordering      10
Leading coefficient      150
Least element      13
Least upper bound      14
Left adjoint      477ff
Left annihilator      444
Left Artinian algebras      451
Left coset      38
Left exact      201
Left Goldie ring      447ff
Left ideal      122
Left inverse of a function      5
Left invertible element      116
Left or right inverse of a function(s)      5
Left orbit      447
Left order      447
Left quasi-regular      426
Left quasi-regular ideal(s)      426
Left quotient ring      447
Length of a series      107 375
Levitsky's Theorem      434
Linear algebra      327ff
linear combination      71
Linear dependence      181
Linear equations      346
Linear functional      203
Linear independence      74 181 291
Linear ordering      13
Linear transformation      170 355ff
Linearly disjoint subfields      318ff
Linearly independent automorphisms      291
Linearly independent elements      74 181
Linearly ordered set(s)      13
Local ring      147
localization      147
Logic      1
Lower bound      14
Lying-over theorem      398
m-system      449
Mac Lane, S.      xiii 325 464
Main diagonal      328
MAP      see "Function"
Maschke's Theorem      454
Mathematical induction      10
Matrices      328ff
Matrices in row echelon form      346
Matrices of a homomorphism      329ff 333
Matrix of a homomorphism      329ff 333
Matrix of a linear transformation      329 333
Matrix of an endomorphism(s)      329ff 333
Matrix relative to a basis      329ff
Maximal element      13
Maximal ideal      127ff
Maximal normal subgroup      108
Maximal subfield      457
Maximum condition      373
McBrien, V.O.      xiii 121
McCoy radical      444ff
McKay, J.H.      93
Meaningful product      27
membership      2
Metacyclic group      99
Middle linear map      207 217
Minimal annihilator      226
Minimal element      373
Minimal left ideal      416
Minimal normal subgroup      103
Minimal polynomial      234 356
Minimal prime ideal      382
Minimum condition      373
Minimum element      13
Minimum polynomial      234
Minor of a matrix      352
Minors of matrices      352
Modular left ideal      417
Module(s)      168ff 371
Modules over a principal ideal domain      218ff
Moebius function      301
Monic morphism      480
Monic polynomial      150
Monk, G.S.      ix 222
Monoid      24
Monomial      152
Monomorphism      30 118 170
Monomorphism in a category      480
Morphism      52 480ff
Multilinear form      349ff
Multilinear function      349ff
Multiple root      161 261
Multiplicative set      142
Multiplicity of a root      161
Mutatis mutandis      xv
N-fold transitive      424
n-th root of unity      see "Unity"
Nakayama's lemma      389
Natural equivalence      468
Natural homomorphism      469
Natural isomorphism      468
Natural number      9
Natural numbers      9
Natural transformation      468ff
Nil ideal      430
Nil of an ideal      379
Nil radical      379 450
Nilpotent element      121 430
Nilpotent endomorphism      85
Nilpotent group      100ff
Nilpotent ideal      430
Noether normalization lemma      410
Noether — Skolem theorem      460
Noetherian modules      372ff 387ff
Noetherian rings      372 387ff
Nonsingular matrix      331
Norm      289
Normal closure      265
Normal endomorphism      84 85
Normal extension field      264ff
Normal series      107ff 375
Normal subgroup      41ff
Normalization lemma      410
normalizer      89
Null set      3
Nullity      335
Nullity of a linear transformation      335
Nullstellensatz      412
Nunke, r.j.      x xiii 93
Object in a category      52
Odd permutation      48
One-to-one correspondence      5
One-to-one function      4
Onto function      5
Opposite category      466
Opposite ring      122 330
Orbit      89
Orbit of a group      24
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте