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Birkhoff G., Mac Lane S. — A Survey of Modern Algebra
Birkhoff G., Mac Lane S. — A Survey of Modern Algebra



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Название: A Survey of Modern Algebra

Авторы: Birkhoff G., Mac Lane S.

Аннотация:

A new edition of the classic undergraduate text introducing abstract algebra using concrete examples. The authors ground their explanations with computational and theoretical exercises to develop the student's "power to think for himself," covering topics such as the role of careful proof in algebra, linear algebra as grounded in geometry, groups as expressions of symmetry, and subgroups and subsystems leading to lattice theory. This volume is a corrected version of the 4th edition and is offered by a new publisher


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Fourth Edition

Год издания: 1977

Количество страниц: 500

Добавлена в каталог: 04.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ring, noncommutative      395
Root field      452ff.
Root field isomorphism      455
Root field, normal      468
Roots of equations      79 101 112ff.
Roots of equations, cubic      102 119 474ff.
Roots of equations, polynomial      101
Roots of equations, quartic      121
Roots of unity      112
Roots of unity, primitive      113
Rotation      125 214
Row equivalent      181ff. 186 246
Row matrix      232
Row rank      242
Row reduced      183
Row space      180
Saddle-point      291
scalar      168
Scalar matrix      229 232
Scalar multiples      see "Product"
Scalar product      168 172 221
Schroeder — Bernstein theorem      387
Schwarz inequality      201
Self-conjugate subgroup      159
Semidistributive laws      375
Separable extension      465
Separable polynomial      465
Set      32 357
Shear transformation      217 247
Signature of quadratic form      289
Signum (of permutation)      319
Similar matrices      264 333
Similarity transformation      132 276
Simple extension of field      421
Simple linear algebra      414
Simultaneous congruences      27 43
Simultaneous indeterminates      73
Simultaneous linear equation      47 182 247 318
Singular matrix      235
Skew-linearity      301
Skew-symmetric matrix      283
Skew-symmetry      301
Solution by radicals      121ff. 480
Solution space      191
Solvable group      479
span      174
Spectrum      265
Square, group of      124ff.
Stable type (equations)      122
Subalgebra (of Boolean algebra)      368
Subdomain      7
Subfield      40
Subgroup      143
Subgroup, normal      159 473
Sublattice      378
SubMatrix      233 320 326
Subring      70 396
Subset      32 357ff.
subspace      173ff. 185ff.
Subspace, affine      306
Subspace, invariant      344
Subspace, parallel      207
Subspace, T-cyclic      344
Substitution property      26 165
Successor function      57
SUM      see also "Addition" "Direct
Sum of ideals      407
Sum of matrices      221
Sum of subspaces      174
Surjection      33
Sylvester's law of inertia      288
Symmetric difference      376
Symmetric group      130 154 481
Symmetric law      3 34 199
Symmetric matrix      283
Symmetric polynomial      154 470
Symmetries      124 131
Tensor product      254
Total matrix algebra      397
Trace of a matrix      336
Transcendental extension      422
Transcendental extension number      422
Transformation      126
Transformation, affine      269ff. 298 330
Transformation, linear      216ff. 241
Transformation, one-one, onto      128
Transformation, orthogonal      273
Transformation, projective      314
Transformation, unitary      300
Transforms, set of      241
Transitive Law      3 9 26 34
Transitive law for inclusion      357 372
Transitive relation      34
Translation      269
Transpose of matrix      219 231 320
Triangle inequality      201
Triangular matrix      229 322
Trichotomy (law of)      9 10
Trigonometric solution of cubic      102
Trisection of angle      434
Two-sided ideal      413
Unary operation      362
Unimodular group      330
union      358 see
Unique factorization      23ff. 80ff.
Unique factorization domain      84
Unique factorization of algebraic integers      450
Unique factorization of Gaussian integers      441
Unique factorization of polynomials      80ff.
UNIT      16 76 439 449
Unit vectors      176
Unitary basis      302
Unitary matrix      300ff. 302
Unitary space      301
Unitary transformations      300
Unity      2 396
Unity for commutative rings      2 69
Universal bounds      359
Universality      254
Upper bounds      96 374
Vandermonde determinant      323
Vector      168ff.
Vector addition      170
Vector equations      188
Vector product      258
Vector space      172ff.
Vector space, dimension of      169 178
Vector, characteristic (eigenvector)      265
Vector, unit      176
Vector, zero      172
Venn diagram      357
Vieta substitution      119
Volume      327
Well-ordering principle      11
Winding number      115
Zero      2 347 see
Zero divisor      6 69
Zero matrix      221
Zero vector      172
1 2 3
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