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| Авторизация |
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| Surowski D. — Workbook in higher algebra |
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| Предметный указатель |
A.C.C. 135
Action, imprimitive 26
Action, permutation 7
Action, primitive 26
Action, regular 9
Acts on 5
Adjoint, left 180
Adjoint, right 180
Algebra 170
algebraic 45
Algebraic closure 50
Algebraic integer 95
Algebraic integer domain 96
Algebraic number 45
Algebraically closed 50
Algorithm 87
Alternating 177
Alternating bilinear form 35
Alternating group 23
Ascending chain condition 135
Associates 79
Atomic domain 85
Automorphism 8
Balanced 161
Basis 116
Bilinear form, alternating 35
Bimodule 165
Butterfly lemma 111
Category theory 180
Cauchy’s Theorem 2
Characteristic 21 30 44
Characteristic polynomial 131
Characteristic subgroup 30
Chinese remainder theorem 76
Closed 53
Closure 53
Cofree R-module 143
Comaximal ideals 76
Commutative graded algebra 171
Commutator 30 32
Commutator subgroup 30
Companion matrix 130
Complete flag 15
Composite 47
Composition series 31 136
Compositum 47
Conjugacy class 5
Content of a polynomial 81
Convolution 152
Coordinate mappinga 115
CYCLE 23
Cycle type 24
Cycles, disjoint 23
Cyclic group 3
Cyclic R-module 122
Cyclotomic polynomial 69
d.c.c 135
Dedekind domain 100
Dedekind Independence Lemma 52
Degree of an element 45 174
Degree of an extension 44 45
Degree, an extension 44
Descending chain condition 135
Determinantal rank 126
Differential 119
Dihedral group 4
Direct sum 113
Discrete valuation ring 108
Discriminant 65
Disjoint cycles 23
divides 79
Divisible abelian group 142
Division algorithm 87
Division ring 139
Double transitivity 9
Elementary components 123
Elementary divisors 123
Equivariant mapping 7
Euclidean Domain 87
Exact 33 92
EXPONENT 122
Extension 44
Extension degree 44
Extension, Galois 54
Extension, purely inseparable 58
Extension, separable 58
Extension, simple 45 73
Exterior algebra 175
F-algebra 152
Field extension 44
Finitely generated 84
Finitely generated, submodule 92
Fixed point set 5
Fixed points 5
Flag 15
Flag, type 15
Fractional ideal 104
Fractional ideal, principal fractional ideal 104
Frattini subgroup 36
Free product 42
Free R-module 145
Free, group 38
Free, module 116
Frobenius automorphism 60
Fundamental theorem of algebra 65
Fundamental Theorem of Algebraic Number Theory 102
Fundamental Theorem of Galois Theory 54
Galois extension 54
Galois group 52
General linear group 14
Generalized quaternion group 20
Generator of a group 3
Generators and relations 39
Graded algebra 174
Graded ideal 174
Graded, algebra 171
Graded-commutative 171
Grassmann space 178
Greatest common divisor 79 80
Group action 5
Group action, faithful 5
Group algebra 152
Group of units 79 181
Group ring 152
Heisenberg group 35
Hilbert basis theorem 84
Homogeneous ideal 174
Homogeneous, elements 174
Homomorphism, module 92
Hopkin’s Theorem 158
Ideal class group 104
Idempotent 149
Idempotents, orthogonal 149
Imprimitivity 26
Imprivitively 26
Inclusion-Exclusion Principle 62
Integral domain 75
Integral group ring 181
Integrally closed 96
Internal direct sum 92 94 114
Invariant basis number 117
Invariant basis number (IBN) 117
Invariant factors 123
Invertible ideal 106 142
Involution 4
| Irreducible 79 136
Irreducible R-module 149
Irreducible, R-module 136
Jacobson radical 155
Jordan canonical form 132
Jordan — Holder theorem 31
k-transitively 27
Kernel of the action 5
Kronecker product 166
Krull topology 64
Lagrange’s Theorem 1
Least common multiple 79 80
Left adjoint 180
Left Artinian 157
Left Noetherian 157
Local ring 138
localization 107
Lower central series 32
Maximal ideal 75
Minimal polynomial 45
Minimal polynomial of a linear transformation 129
Minor 126
Modular law 93 111
Module 91
Module homomorphism 92
Monomorphism 181
Nakayama’s Lemma 157
Near field 63
Nil ideal 156
Nilpotent element 78
Nilpotent, element 156
Nilpotent, group 32
Nilpotent, ideal 156
Noether Isomorphism Theorem 111
Noetherian module 135
Noetherian, module 93
Noetherian, ring 84
Norm map 61
Normal closure 39
Normal series 31
Orbit 5
Orbit-Stabilizer Reciprocity Theorem 5
Order 2 121
Order, infinite 2
Overring 107
p-group 6
p-part 12
Perfect 59
Permutation isomorphic 7
Plucker embedding 178
Pointwise 152
Polynomial, separable 58
Primary decomposition theorem 132
Primary ideal 77
Prime, element 79
Prime, ideal 75
primitive 26
Primitive element 73
Primitive Element Theorem 73
Primitive polynomial 81
Principal ideal 76
Principal ideal domain 84
Prinicpal fractional ideal 104
Projection mappings 115
Projective 141
Projective general linear group 14
Projective space 15 178
Projective special linear group 14
Purely inseparable 58
Purely inseparable, element 58
Quadratic integer domains 96
Quasi-dihedral group 20
Quaternion group 20
Quaternion group, generalized 20
Rank 117
Rational canonical form 130
Regular action 9
Regular normal subgroup 28
Relations 39
Relations matrix 125
Relatively prime ideals 76
Representation 152
Residual quotient 77
Right adjoint 180
Right Artinian 157
Right Noetherian 157
Root tower 72
Schreier refinement theorem 136
Second isomorphism theorem 111
Semi-direct product 17
Semi-direct product, external 18
Semi-direct product, internal 17
Semidihedral group 20
Semisimple 133
Semisimple, linear transformation 139
Semisimple, R-module 148
Semisimple, ring 157
Separable 58 73
Separable element 58
Separable extension 58 73
Separable polynomial 58
Separable, element 73
Short exact sequence 92
Short exact sequence, splitting 118
Short exact sequence, splitting of 95
SIMPLE 136
Simple field extension 45
Simple R-module 136
Simple radical extension 72
Simple ring 150
Smith equivalent 125
solvable 31
Solvable by radicals 72
Solvable group 31
Special linear group 14
Split short exact sequence 118
Splits 95
Splitting field 46 49
Stabilizer 5
Stable 54
Subgroup, characteristic 21 30
Submultiplicative algorithm 87
Subnormal series 31
Sylow subgroup 12
Symmetric algebra 174
Symmetric group 3
System of imprimitivity 26
System of imprimitivity, non-trivial 26
System of imprimitivity, trivial 26
Tensor algebra 173
Tensor product 161
Third isomorphism theorem 111
Torsion element 121
Torsion submodule 121
Torsion-free 121
Totally discontinuous 64
Transitive 7
Transposition 23
U.F.D. 79
Unique factorization domain 79
UNIT 79
Valuation ring 108
Word problem 40
Zassenhaus lemma 111
Zero-divisor 75
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