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Jacobson N. — Lectures in Abstract Algebra, Vol. 2
Jacobson N. — Lectures in Abstract Algebra, Vol. 2

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Название: Lectures in Abstract Algebra, Vol. 2

Автор: Jacobson N.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 290

Добавлена в каталог: 13.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Algebra      26 225
Algebra of linear transformations      36
Algebra, free      210—211
Algebra, Grassmann      211
Bases      15
Bases of infinite dimensional vector spaces      239
Bases, Cartesian      173
Bases, change of      42
Bases, complementary      53
Bases, matrix of      15
Bases, unitary      190
Bilinear forms      137
Bilinear forms, matrices of      138
Bilinear forms, non-degenerate      140
Burnside’s Theorem      276
Canonical matrices, classical      73 94
Canonical matrices, Jordan      70 93
Chain conditions      28
Characteristic polynomial      98 103
Characteristic roots      104
Characteristic roots of real symmetric matrices      180
Characteristic spaces      182
Characteristic vector      100 186
Cogredience (of matrices)      149
Commutative sets of linear transformations      133—135
Complete reducibility of a single linear transformation      129
Complete reducibility of sets of linear transformations      124
Complete reducibility, orthogonal      177
Composition series      120
Conjugate space      52
Conjugate space of infinite dimensional vector space      244
Cyclic linear transformations      69
Cyclic linear transformations, elementary divisors      73
Decomposability of a single linear transformation      129
Decomposability of sets of linear transformations      122
Dense rings of linear transformations      259—264
Dimensionality of free modules      89
Dimensionality of infinite dimensional vector spaces      241 244
Dimensionality of vector spaces      10 14
Direct product of linear transformations      203
Direct product of spaces      201
Direct sum of submodules      85
Direct sum of subspaces      30
Duality of infinite dimensional vector spaces      253
Duality of vector spaces and conjugate spaces      54
Elementary divisors      73 94
Endomorphisms of cyclic module      106
Endomorphisms of finitely generated module for principal ideal domain      108
Exponential function      197
Extension of field of vector space      221
Factor space      25
Finitely generated commutative groups      88
Frobenius theorem      102 111
Gaussian domain      101
General density theorem      274
Geometry Euclidean      172
Geometry unitary      190
Group, full linear      46
Group, unitary      191
Hamilton — Cayley theorem      101
Ideals in ring of linear transformations      230 232 256
Ideals, elementary divisor ideals      94
Ideals, invariant factor ideals      92
Ideals, order ideal      85
Invariant factors      84
Irreducible algebras of linear transformations      274
Irreducible set of endomorphisms      259
Irreducible set of linear transformations      116
Isomorphisms in infinite dimensional vector spaces      264
Isomorphisms of rings of linear transformations      233
Jordan — Holder theorem      127
Kronecker delta      17
Kronecker product of algebras      225
Kronecker product of infinite dimensional vector spaces      256
Kronecker product of linear transformations      211
Kronecker product of matrices      213
Kronecker product of vector spaces      208
Krull — Schmidt theorem      127
Lattices      26
Lattices, complemented      27 125
Lattices, modular      27
Linear dependence      10
Linear equations      47
Linear function      32 51
Linear transformations commuting with a given one      110
Linear transformations in right vector spaces      49
Linear transformations induced in invariant subspace and factor space      117
Linear transformations, addition of      32
Linear transformations, analytic functions of      194
Linear transformations, definition      32
Linear transformations, matrix of      36—37
Linear transformations, minimum polynomial of      65
Linear transformations, normal      184
Linear transformations, nullity of      44
Linear transformations, orthogonal      178
Linear transformations, polar factorization      188 192
Linear transformations, power series in a linear transformation      195
Linear transformations, product of      34
Linear transformations, rank of      44
Linear transformations, semi-definite      186
Linear transformations, skew      178
Linear transformations, symmetric      178
Linear transformations, transpose of      56 142
Linear transformations, unitary      191
Matrices      15 18
Matrices in infinite dimensional vector spaces      243
Matrices of bases      15
Matrices of bilinear forms      138 149
Matrices of linear transformations      37
Matrices of transpose      58
Matrices, addition of      39
Matrices, column rank of      22
Matrices, elementary divisors of      94
Matrices, elementary matrices      19 82
Matrices, equivalence of      42 79
Matrices, Hermitian      150 191—192
Matrices, invariant factors of      84
Matrices, multiplication of      39
Matrices, non-singular      16
Matrices, normal      185
Matrices, normal form of      84
Matrices, orthogonal      175
Matrices, row rank of      22
Matrices, similarity of      43
Matrices, symmetric      179
Minimum polynomial      65 98
Minimum polynomial, degree of      69
Modules      7
Modules, cyclic      85
Modules, equivalence of      8
Modules, factor      88
Modules, finitely generated      8 76 85
Modules, free      8 76
Modules, generators of      8
Modules, submodule      7
Partially ordered set      26
Primary components      130—132
Product group of vector spaces      200
Projection      60
Projection, orthogonal      60
Projection, supplementary      60
Rank in infinite vector spaces      256
Rank of a set of vectors      22
Rank of linear transformations      44
Rank, column rank of matrices      22
Rank, determinantal rank      23
Rank, row rank of matrices      22
Reducibility of a single linear transformation      128
Reducibility of sets of linear transformations      116
Ring of linear transformations, anti-automorphism      267
Ring of linear transformations, automorphism      237
Ring of linear transformations, center of      114
Ring of linear transformations, finite topology in      248
Ring of linear transformations, isomorphisms      233 266
Ring of linear transformations, left ideals in      230
Ring of linear transformations, right ideals in      232
Ring of linear transformations, simplicity      227
Ring of linear transformations, two-sided ideals in      256
Rotation      179
Scalar products      148
Scalar products, alternate      160
Scalar products, hermitian      150
Scalar products, non-degenerate      151
Scalar products, totally regular      167
Scalar products, weakly hermitian      268
Schmidt’s orthogonalization process      174
Schur’s lemma      271
Subspaces of infinite dimensional vector spaces      242
Subspaces, cyclic      66
Subspaces, direct sum      30
Subspaces, independent      28
Subspaces, invariant      66 115
Subspaces, isotropic      151
Subspaces, total      251
Sylvester’s theorem      156
Tensors      213
Tensors, contraction of      215
Tensors, skew symmetric      218
Tensors, symmetry classes      217
Topological space      248
Trace of a matrix      99 103 216—217
Transitivity      272
Vector spaces, abstract (finite dimensional)      3
Vector spaces, conjugate space of      53
Vector spaces, cyclic      69
Vector spaces, dimensionality of      10 14
Vector spaces, infinite dimensional      238
Vector spaces, Kronecker product of      208
Vector spaces, right      6
Vector spaces, two-sided      204
Vectors, linear dependence      10
Vectors, order of      67
Vectors, product      1
Vectors, scalar product      1
Vectors, sum      1
Witt’s Theorem      162
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