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Авторизация |
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Поиск по указателям |
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Albert A.A. — Structure of algebras |
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Предметный указатель |
-array 130
-basis 14
Absolute irreducibility 121
Algebraic number theory lemmas 147
Algebras 3
Algebras of order one 20
Algebras with a total matric subalgebra 19
Algebras, characteristic function of 11 16 122
Algebras, components of 28
Algebras, degree of 16
Algebras, equivalence of 3
Algebras, equivalence to matric algebras 11
Algebras, general quantity of 16
Algebras, principal degree of 16
Algebras, reciprocal 3
Applications of the Galois theory 63
Archimedean valuations 145
Automorphisms 7
Automorphisms of a direct product 85
Automorphisms of a field 35
Automorphisms of a normal simple algebra 51
Automorphisms of an unramified field 141
Automorphisms, extension of equivalences to 54
Automorphisms, inner 9 49
Automorphisms, reciprocal 8
Basis of integers 130
Basis of total matric algebra 7
Bibliography 193ff
Centrum 6
Centrum of a direct sum 30
Centrum of a simple algebra 41
Centrum of an involutorial algebra 153
Centrum, scalar extension of 35
Characteristic function 11 16 122
Class group 59
Classes of algebras 58
Commutative semi-simple algebras 39 40 44
Commutator algebra 6
Commutator of equivalent subalgebras 56
Completely ramified algebras 137
Components of algebras 28
Components of representations 115
COMPOSITES 34
Construction of crossed products 68 182
Construction of involutions 157
cosets 27
Crossed products 66
Crossed products of degree four 187
Crossed products, construction of 68 182
Crossed products, direct products of 71
Crossed products, equivalence of 71
Crossed products, involutorial 158
Crossed products, normalized 73
Crossed products, scalar extension of 73
Cyclic algebras 74
Cyclic algebras, direct factorization of 100
Cyclic algebras, direct powers of 75 97
Cyclic algebras, direct products of 74
Cyclic algebras, equivalence of 75
Cyclic algebras, exponents of 98
Cyclic algebras, total matric 74
Cyclic fields 35
Cyclic p-algebras 107
Cyclic semi-fields 83
Cyclic semi-fields, direct products of 86
Cyclic semi-fields, norms in 84
Cyclic systems 88
Cyclic systems, group of 89
Cyclic systems, powers of 91
Decomposable GR-matrices 126
Decomposable representations 115
Degree of a cyclic system 88
Degree of a normal simple algebra 43
Degree of a splitting field 60
Degree of an algebra 16
Diagonal algebras 20 44 79
Diagonal direct factors 82
Difference algebra 28
Difference group 27
Direct factorization of algebras 43
Direct factorization of cyclic algebras 100
Direct factorization of normal division algebras 77
Direct factorization, uniqueness of 85
Direct powers 6
Direct powers of cyclic algebras 75 97
Direct powers of division algebras 75
Direct products 5
Direct products of crossed products 71
Direct products of cyclic algebras 75
Direct products of normal algebras 41
Direct products of normal division algebras 52
Direct products of total matric algebras 7 50
Direct sum 28
Direct sum, centrum of 30
Direct sum, ideals of 29
Direct sum, semi-simple 39
Division algebras 14
Division algebras, commutative 15
Division algebras, direct product of 52
Division algebras, normal 41
Division algebras, ramified 137
Division algebras, subalgebras of 15
Division p-adic algebras 137
Enveloping algebra 113
Equivalence of algebra-group pairs 65
Equivalence of algebras 3
Equivalence of crossed products 71
Equivalence of cyclic algebras 75
Equivalence of representations 110
Exponent of a field 33
Exponent of normal simple algebra 76
Exponent of p-adic algebra 144
Exponent of p-algebra 109
Exponent of rational division algebra 150
Extension of equivalences 54
Factor sets 67
Fields, inseparable 32 101
G-irreducible algebra 78
General quantity 16
Generalized cyclic algebras 93
Generalized cyclic algebras, Riemann matrices 126
Generating automorphism 35
Generating automorphism of a cyclic semi-field 83
Group of classes 59
Group of cyclic systems 89
Group-algebra pairs 65
Grunwald lemma 148
Hensel lemma 136
Ideals 22
Ideals of a direct sum 29
Ideals of a nilpotent algebra 22
Ideals of a p-adic algebra 133
Ideals, maximal 38
Ideals, prime 134
Idempotents 20
Idempotents, existence of 23
Idempotents, primitive 26
Idempotents, principal 25
Idempotents, rank of 50
Idempotents, similar 50
Impure GR-matrices 126
Impure representation algebras 114
Impure Riemann matrices 188
Index of a class 58
Index of a nilpotent quantity 22
Index of a normal simple algebra 58
Index of a p-adic extension 148
Index of an algebra 4 5
Index reduction factor 59
Inseparable 32
| Integers 129
Integral basis 130
Integral domains 129
Intersection of ideals 22
Intersection of left ideals 21
Intersection of linear sets 1
Invariant subspace 113
Involutions 151
Involutions of direct products 155
Involutions of normal simple algebras 156
Involutions of similar algebras 156
Involutions of simple algebras 154
Involutions, construction of 157
Involutions, kinds of 153
Involutorial algebras 151
Involutorial algebras, centrum of 153
Involutorial algebras, symmetric subfields of 157
Involutorial crossed products 158
Involutorial cyclic algebras 160
Involutorial quaternion algebras 161
Involutorial rational algebras 161 162
Isomorphic matrices 126 188
J-skew quantities 152
J-symmetric quantities 151
Least representation algebra 61
Left ideal 21
Left ideal, simple left ideal 23
Left linear set 14
Left multiplications 12
Linear sets 1
Linear sets, products of 3
Linear sets, sums of 1
Linear sets, supplementary 2
Linear sets, zero 1
Linear transformations 9 111
Matric basis 7
Matric representation 111
Maximal -array 130
Maximal ideal 38
Maximal subfields 56 85
Minimum function 11 13 16 122
Multiplication algebras 128 189
Multiplication algebras, structure of 168
Multiplication algebras, subfields of 166
Nilpotent algebra 22
Non-associative algebras 188
Non-singular quantity 13
Non-singular transformation 10
Norm condition 184
Norm function 18 122
Normal algebras 6
Normal algebras over centrum 15
Normal algebras, direct products of 41
Normal direct factors 41
Normal division algebras 41
Normal division algebras of degree 179
Normal division algebras of degree four 179
Normal division algebras of degree three 177
Normal division algebras of low degrees 178
Normal division algebras of prime degree 177
Normal division algebras, direct factorization of 77
Normal division algebras, exponent of 77
Normal division algebras, maximal subfields of 57
Normal division algebras, powers of 75
Normal division algebras, primary 77 174
Normal simple algebras 41
Normal simple algebras as direct factors 51
Normal simple algebras of degree two 146
Normal simple algebras, automorphisms of 51
Normal simple algebras, commutator of subfields of 53
Normal simple algebras, degree of 43
Normal simple algebras, direct product with reciprocal of 47
Normal simple algebras, exponent of 76
Normal simple algebras, index of 58
Normal simple algebras, involutions of 156
Normal simple algebras, maximal subfields of 56
Normal simple algebras, metacyclic subfields of 63
Normal simple algebras, scalar extension of 43 56 59
Normal simple algebras, simple subalgebras of 53
Normal simple algebras, splitting fields of 60
Normal simple algebras, subfields of 53
Norms in cyclic semi-fields 84
Order of a p-adic integer 132
Order of a p-adic quantity 133
Order of a product of sets 4
Order of an algebra class 76
Orthogonal quantities 20
p-adic division algebras 132
P-adic fields 138 151
p-adic normal simple algebras 142
p-algebras 104
Pairwise orthogonal 20
Peirce decompositions 24
Powers of algebras 4 5 75 97
Powers of cyclic systems 91
Primary algebra 77 174
Prime ideal 134
Primitive idempotent 26
Principal degree 16
Principal function 16
Principal idempotent 25
Principal matrix 165 188
Principal norm 18 124
Principal theorem 47
Principal trace 18 124
Products of classes 58
Products of cyclic systems 89
Products of factor sets 68
Products of ideals 22
Products of linear sets 3
Properly nilpotent quantity 24
Pure GR-matrix 126
Pure inseparable 32 101
Pure representation algebra 114
Pure Riemann matrix 188
Quadrate algebra 17
Quadratic field 145
Quaternion algebras 145
Radical 23
Radical of 25
Radical of a direct sum 29
Ramification order 135
Ramification order of a division algebra 136
Ramification order of a prime ideal 148
Rank of idempotents 50
Rational division algebras 129
Rational division algebras, determination of 149
Rational division algebras, equivalence of 150
Rational division algebras, exponent of 150
Rational involutorial algebras 161
Real quaternion algebras 146
Real Riemann matrices 190
Reciprocal algebras 3
Reduced degree 33
Reduced field 173
Reduced norm 122 124
Reduced trace 122 124
Reducible algebras 28
Reducible representations 113
Reducible representations, components of 116
Regular quantity 13
Regular representation 11
Representation of algebras 110
Representation of field by algebra 60
Representations 111
Representations, absolutely irreducible 121
Representations, decomposable 115
Representations, fully decomposable 118
Representations, reducible 113
Residue-class degree 135
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