Shafarevich I.R., Kostrikin A.I. (ed.) — Basic Notions of Algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Shafarevich I.R., Kostrikin A.I. (ed.) — Basic Notions of Algebra

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Название: Basic Notions of Algebra

Авторы: Shafarevich I.R., Kostrikin A.I. (ed.)

Аннотация:

From the reviews: "... This is one of the few mathematical books, the reviewer has read from cover to cover ...The main merit is that nearly on every page you will find some unexpected insights... " Zentralblatt für Mathematik "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition... which transports the reader effortlessly across the whole spectrum of algebra...Shafarevich's book - which reads as comfortably as an extended essay - breathes life into the skeleton and will be of interest to many classes of readers; certainly beginning postgraduate students would gain a most valuable perspective from it but... both the adventurous undergraduate and the established professional mathematician will find a lot to enjoy..."

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Рубрика: Математика/Алгебра/Абстрактная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 258

Добавлена в каталог: 05.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Quotient ring (= residue class ring)      28
Quotient sheaf      226
Radical extension $K(\sqrt[n]{a})$       180
Rank of a module rank M      34 41
Rank of an algebra over a field      63 92
Rational fraction      12
Rational function      12
Rational function field K(x), $K(x_1, \cdots, x_n)$       13
Rational function field of a curve or variety K(C)      14
Real part of a quaternion Re(q)      65
Reduced suspension SX      210—211 231 232
Reflection      97 98 119
Regular action (left-, right-)      105 193
Regular polyhedron      110—114 158 169
Regular representation      77 78 170 176—177 209
Remak, R.      153
Representable functors ,       208—209
Representation of $\mathfrak{S}_3$ and octahedral group      167
Representation of a group      75—76 160—177
Representation of Abelian groups      163—165 170 173
Representation of an algebra      75
Representation of classical complex Lie groups      174—177
Representation of compact Lie groups      167—174 185—188
Representation of finite groups      119 163 240
Representation of semisimple ring      81—83 88—89
Representation of SO(3)      174
Representation of SO(4)      171—172
Representation of SU(2)      172—174 185—187
Residue class mod I      28
Ricci (trace-free) tensor      172
Ricci, C.G.      172
Riemann surface      31 58 126 131 137—138 226 229 241
Riemann — Roch theorem      229—230 234 241
Riemann, G.F.B.      31 58 72 169 172 224 230
Right coset, right ideal, right invariant, right regular      see coset ideal invariant regular
Rigid body motions      140 195 198
Ring      17 62
Ring axioms      62
Ring of bounded operators on Banach space      62 69 87
Ring of differential operators      63 69 73
Ring of linear transformations:      see endomorphism ring matrix coordinate- semisimple-)
Roch, G.      230
Rotation      110 112 140—142
Row and column operations      43 237
Ruler-and-compass construction      50
Salt NaCl      98
Schoenflies, A.M.      242
Schur's lemma      77
Schur, I.      77
Section of a family of vector spaces      40
Seifert, H.      241 243
Semidirect product of groups      223
Semigroup with unit      206 230
Semisimple module or ring      79 81 90 103 166 167 169 175 184
Serre, J.-P.      240
Set with operations      4 11 17 100
Sheaf      225—230
Sheaf associated with a divisor on a Riemann surface $\mathscr{F}_D$       226 229
Sheaf cohomology $H^n(X, \mathscr{F})$       225—230
Shmidt, O.Yu.      153
Short exact sequence      218
Similar lattices      132
Simple algebraic groups      157
Simple central algebra      92 103—104
Simple compact Lie groups      157
Simple complex Lie groups      157 177
Simple finite groups      159
Simple group      154 155 158
Simple Lie algebra      192 197
Simple Lie groups      157 197
Simple module or ring      72 73 77 81 82 84
simplex      214
Simply connected      137 142
Singer, I.M.      234
Singular point of a variety      54
Skew field:      see division algebra
Skew-isomorphic (= opposite) ring      67
Skew-isomorphism of rings      67 71
Smash product $X \wedge Y$       210
Solvable group      155—157 180
Solving a differential equation by quadratures      181—182
Solving an equation by radical      180
Soule, C.      243
Special linear group SL(n, k)      144 149 195
Special linear Lie algebra sl(n, K)      190—191 195
Speiser, A.      240
Spinor group Spin(n), Spin(p, q)      146 149
Sporadic simple groups      159
Stabiliser subgroup of a point       100 104 106 128
Stammbach, U.      241
Stapelia variegata      130
Stokes'theorem      216—217
Stokes, G.G.      216
Structure constants of an algebra      63 192 194
Subcomplex      217

Subfield      12 30
Subgroup      104. See also Lie subgroup normal
Submanifold      32 200—201
Submodule      35
Submodule generated by a system of elements      36
Subrepresentation (= invariant subspace)      75 76 162 175
Subring      17 63
Subsheaf      225
Sum in a category      202 207
Sum of extensions of modules      103
Superalgebra (= $\mathbb{Z}/2$ -graded algebra)      70 216
Suslin, A.A.      241 243
Suspension $\Sigma X$       210—211 232
Switzer, R.M.      241
Symbol of an elliptic operator $\sigma_{\mathscr{D}}$       234
Symmetric group $\mathfrak{S}_n$       108—109 119 122 139 162 180—181
Symmetric power of a module S'M      39 184
Symmetric square of a module       39
Symmetric—function      98 180
Symmetry      96—99 158 161 169 174 177 242
Symmetry breaking      174 185—187
Symmetry group of a crystal      97—98 126 242
Symmetry group of a lattice (Bravais group)      115—118 127
Symmetry group of a molecule      97 113
Symmetry group of a polynomial      98
Symmetry group of a regular polyhedron      111—112 158
Symmetry group of an ornament      97 128 242—243
Symmetry group of physical laws      98 99 242
Symmetry group of the n-cube       123
Symplectic group $Sp(2n, \mathbb{C})$       148
Tamagawa number      151
Tamagawa, T.      151
Tangent space      51—54
Taylor, B.      52 56
Tensor algebra of a vector space T(L)      67—68 183
Tensor of type $(p,q)T^{p,q}$       39
Tensor power $T^{\gamma}(M)$ , $T^{\gamma}(\rho)$       38 67 166 207—208
Tensor product of algebras or rings      92 104 166 204 207
Tensor product of modules      36—38 166 170 208
Tensor product of representations      166 167
Tensor, covariant or contravariant      38 39
Tetrahedral group $T \cong \mathbb{A}_4$       97 111—112 167
tetrahedron      97 110—112 158
The Monster      159
Threlfall, W.      241 243
Topology, topological space      102 125 136—140 213 225
Torsion element or module      42 43
Torus      143 243
Trace      88—89 90 173 195
Transcendence degree tr deg L/K      47
Transformation group      96 100 192 209 240
Transitive action or transformation group      100 106 143 169
Translation in a Lie group      142 195
Trivial family of vector spaces      230
Tsen's theorem (on division algebras over K(C))      91
Tsen, C.T.      91
Twistor space      66
Two-sided ideal:      see ideal
Ultraproduct of fields      32
Uniformisation of Riemann surfaces      126 131 137—138
Unique factorisation      22 61
Unique factorisation domain (UFD)      22 26
Unitary groups U(n), SU(n), SU(p,q), PSU(n)      144 158
Unitary Lie algebra u(n), su(n)      191 196
Unitary representation      169 177
Unitary symplectic group SpU(n)      145
Unitary symplectic Lie algebra spu(3n, K)      191
Unitary trick      175—176
Universal cover      138 142 182—183 197
Universal mapping property      37 202—204 207
Unramified cover of a space      125 142 182—183
Valuation of a field      57—61
Van der Waerden, B.L.      239 243
Vector bundle      230
Vector field      33 36 39 40 53 144 189 190 191 193 226 233
Vector space with a linear transformation      34 42 43 77 80 103
Vessiot, E.      181
von Helmholtz, H.      168 169 243
von Neumann, J.      242
Weber, H.F.      239 241
Wedderburn — Remak — Shmidt theorem      153
Wedderburn's theorem (on finite division algebras)      91
Wedderburn's theorem (on semisimple rings)      83 104
Wedderburn, J.H.M.      83 91 153
Weierstrass approximation theorem      170
Weierstrass preparation theorem      22
Weierstrass, K.T.W.      22 170
Weil, A.      239 241
Weyl tensor      172
Weyl, C.H.H.      6 172 193 240 242 243
Word      134
Word problem (= identity problem) for groups      135—136
Zeeman, P.      174
Zeta-function      238
Zhelobenko, D.P.      240 243
Zorn, M.A.      29

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