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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
Orbit of a permutation      47
Orbit of an element      35 220
Order ideal      220
Ordered pair      6
Ordering by extension      18
Orthogonal idempotents      135 439
p-group      93
p-primary      380 384
P-primary ideal      380
P-primary submodule      384
p-radical      425
P.I.D.      see "Principal ideal domain"
Pair formation      6
Partial orbit      13
Partial ordering      13
Partially ordered set(s)      13
Partition      7
Perfect field      289
Permutation(s)      26 46ff
Polynomial(s) in n indeterminates      151
Power axiom      3
Power series      154ff
Power set      3
Presentation of a group      67
Primary decomposition      381 383ff
Primary ideal      380ff
Primary rational canonical form      361
Primary submodule      383ff
Primary submodule(s)      383ff
Prime element      136
Prime ideal      126ff 377ff
Prime integer      11
Prime radical      379 444ff
Prime ring      445ff
Prime subfield      279
Primitive Element Theorem      287 288
Primitive ideal      425
Primitive polynomial      162
Primitive ring      418ff
Primitive root of unity      295
Principal ideal      123
Principal ideal domain      123
Principal ideal ring      123
Principle of Mathematical Induction      10
Principle of transfinite induction      14
Principle of well ordering      14
Product category      467
Product in a category      53ff
Product map      228
Product of cardinal number(s)      16
Projective module      190ff
Proper class      2
Proper ideal      123
Proper refinement      108 375
Proper subgroup      32
Proper values      367
Proper vectors      367
Pruefer domain      409
Pullback      170 484
Purely inseparable element      282
Purely inseparable extension      282ff
Purely inseparable extension field      282ff
Purely transcendental extension      314
Purely transcendental extension field      314
Quasi-inverse      426
Quasi-regular      426
Quaternion group      33 97 99
Quotient class      6
Quotient field      144
Quotient group      42ff
Quotient ring      125 144ff 447
r-cycle      46
R-module      see "Module"
Rad I      379
Radical extension field      303ff
Radical property      425
Radical ring      429
Range of a function      3
Rank of a free abelian group      72
Rank of a free module      185
Rank of a homomorphism      335ff 339
Rank of a linear transformation      335ff
Rank of a matrix      337ff
Rank of matrices      336 337
Rank of module(s)      185
Rank or dimension of a free module      185
Rational canonical form      360
Rational function      233
Rationals modulo one      27
Recursion theorem      10
Reduced Abelian group      198
Reduced group(s)      198
Reduced primary decomposition      381 384
Reduced row echelon form      346
Reduced word      64 68
Refinement of a series      108 375
Reflexive module      205
Reflexive relation      6
Regular element      447
Regular function      412
Regular left ideal      417
Regular ring(s)      442
Relation      6 66
Relative complement      3
Relative dimension      245
Relative index      245
Relatively prime elements      140
Relatively prime integers      11
Relatively prime ring elements      140
Remainder theorem      159
Representable functor      470ff
Representation      470
Resolvant cubic      272
Restriction      4
Right adjoint      477
Right annihilator      444
Right coset      38
Right Goldie ring      447
Right ideal      122
Right inverse of a function      5
Right invertible element      116
Right quasi-regular      426
Right quotient ring      447
Ring of Polynomial(s)      149ff 151 156
Ring(s)      115ff 371ff 414ff
Ring(s) extensions      394ff
Ring(s) of formal power series      154ff
Ring(s) of quotients or fractions      144ff
Root of unity      294
Roots of Polynomial(s)      160
Row echelon form      346
Row rank      336 339
Row space      336
Row spaces of matrices      336
Row vector      329
Ruler and compass constructions      238
Russell's paradox      2
Scalar matrix      328
Schreier's theorem      110 375
Schroeder — Bernstein theorem      17
Schur's lemma      419
Second isomorphism theorem      44 126 173
Secondary matrices      340
Secondary matrix      340
Semidirect product      99
Semigroup      24
Semiprime ring      444ff
Semisimple module      437
Semisimple ring      429 434ff
Separable degree      285ff
Separable element      261
Separable extension      261 282ff 324
Separable extension field      261 282ff 324
Separable polynomial      261
Separably generated extension      322
Separably generated extension field      322
Separating transcendence base      322
SEQUENCE      11
Short exact sequence      176
Short Five Lemma      176
Sign of a permutation      48
Similar matrices      332 355ff
Simple components      440
Simple extension field      232
Simple group      49
Simple module      179 375 416ff
Simple ordering      13
Simple ring      416ff
Simple root      161 261
Singleton      6
Skew-symmetric matrices      335
Skew-symmetric matrix      335
Skew-symmetric multilinear form      349
Solvable by radicals      303
Solvable group      102ff 108
Solvable series      108
span      181
Spectrum      378
Split exact sequence      177
Splitting field      257ff
Splitting fields      257ff
Stabilizer      89
Stable intermediate field      250
Standard basis      336
Standard basis of $R^{n}$      336
Standard n-product      28
Subalgebra      228
subclass      2
Subdirect product      434
Subdirectly irreducible ring      442
Subfield(s) generated by a set      231 232
Subgroup(s)      31ff
Subgroup(s) generated by a set      32
Subgroup(s) generated by groups      33
Submodule(s)      171
Submodule(s) generated (or spanned) by a set      171
Subnormal series      107ff
Subring      122
Subring generated by a set      231 232 395
Subset      3
subspace      171
Substitution homomorphism      153
Sum (=coproduct)      54ff
Sum of cardinal number(s)      16
Sum of module(s)      171
Sum of submodules      171
Surjective function      5
Swords, R.J.      xiii
Sylow p-subgroup      94
Sylow subgroup(s)      94
Sylow theorems      92ff
Symmetric group      26 46ff
Symmetric matrices      335
Symmetric matrix      335
Symmetric multilinear function      349
Symmetric rational function      252ff
Symmetric relation      6
Symmetries of the square      26
Tensor product      208ff
Tensor product of algebras      229
Tensor product of module(s)      208ff
Terminal object      57
Third isomorphism theorem      44 126 173
Torsion group      78
Torsion module      179 220
Torsion subgroup      78
Torsion submodule      179 220
Torsion-free group      78
Torsion-free module      220
Total degree      157
Total ordering      13
Trace      289 369
Trace of an endomorphism(s)      369
Trace of matrices      369
Transcendence base      313ff
Transcendence basis      313ff
Transcendence degree      316
Transcendental element      233
Transcendental extension      233 311ff
Transcendental extension field      233 311ff
Transfinite induction      14
Transitive relation      6
Transitive subgroup      92 269
Transitive subring      424
Translation      88
Transpose of a matrix      328
Transposition      46
Triangular matrices      335
Triangular matrix      335
Trichotomy Law      18
Trichotomy law for cardinal number(s)      18
Trivial ideal      123
Trivial module(s)      170
Trivial subgroup(s)      32
Two sided inverse of a function      5
U.F.D.      see "Unique factorization domain"
Underlying set      55
union      3
Unique factorization      137ff
Unique factorization domain      137
UNIT      116
Unit map      228
Unitary module      169
Universal element      470
Universal mapping property      9 57
Universal object      57
Upper bound      13
Valuation domain      409
van Dyck's Theorem      67
Variety      409
Vector space      169 180ff
von Neumann regular ring      442
Weak direct product      60 62
Weak direct product of group(s)      60 62
Wedderburn — Artin Theorems      421 435
Wedderburn's Theorem on finite division rings      462
Well ordered set      13
Well Ordering Principle      14
Word      64 68
Yoneda, N.      472
Zassenhaus lemma      109 375
Zero      409
Zero divisor      116
Zero element      115
Zero matrix      328
Zero morphism      482
Zero object      481
Zero of a polynomial      160
Zorn's lemma      13
1 2 3
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