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| Авторизация |
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| Jacobson N. — Structure of rings (American mathematical society colloquium publications. Volume XXXVII) |
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| Предметный указатель |
 -regular  -module 172
Adjoint of semi-linear transformation 72
Algebraic algebras 19 210 218 236—237 240—260
Algebraic element 19
Algebras of uniform index 244
Algebras over commutative rings 16
Algebras over commutative rings, over fields 18—20
Annihilator 92
Ascending chain condition 198
Bilinear form 69
Bilinear form, non-degeneracy of 70
Biregular ring 210
Boolean ring 210
Brauer group 120—122 152—156
Cartan-Brauer — Hua theorem 186
Center of semi-simple ring with minimum condition 43
Centralizer of subring 24
Centralizer of subring of completely reducible module 124—126 130—132
Centralizer of subring of irreducible module 26
Centralizer of subring of module 24
Centralizer of subring of right ideal  51
Centralizer of subring of set of linear transformations 32
Centralizer of subring of simple algebra of linear transformations 132
Centralizer of subring of strictly cyclic module 25
Centroid 107
Centroid of simple algebra 108
Closure in finite topology 32
Closure in finite topology of set of primitive ideals 203
Commutativity theorems 183—185 217—222
Completely primary ring 56
Conjugate space 66
Conjugate space, dimension of 68
Conjugate space, total subspaces of 68
Degree of commutativity 228
Density of subdirect sum 15
Density theorems for irreducible modules 28 31
Density theorems for irreducible modules for completely reducible modules 127
Density theorems for irreducible modules for one-sided ideals 33
Derivation 85
Derivation,  -derivation 170
Derivation, constants relative to 174
Derivation, extension theorems for 86 151—152
Derivation, higher 171
Descending chain condition for right ideals 38
Differential transformation 87
Dimension of completely reducible module 63
Dimension of completely reducible module of distinguished rings of endomorphisms 138—139
Dimension of completely reducible module of ring relative to subring which is primitive with minimal right ideals 135
Dimension of completely reducible module, left and right dimensions 158 164 175
Dimension of completely reducible module, relative to division subring 157 158
Direct sum complete direct sum of rings 14
Direct sum complete direct sum of rings, discrete direct sum of rings 14
Direct sum complete direct sum of rings, subdirect sum of rings 13—16
Distinguished ring of endomorphisms 127
Distinguished ring of endomorphisms, associated with division subrings 159
Division ring extensions 187—192
Dual vector spaces 69
Enveloping algebra 201
EXPONENT 156
Extension of isomorphisms 150 162
Extension of ring of operators of an algebra 103
Factor set 84 153
Finite Galois theory for division rings 163—165
Fundamental theorem for ring of linear transformation 149
Fundamental theorems for division rings 165 168
Galois  -modules 142—144
Galois theory Concepts of Galois theory 140—142
Galois theory Concepts of Galois theory for the ring of linear transformations 140—152
Height 135
Ideal of matrix rings 40
Ideal, in semi-simple ring with minimum condition 43
Ideal, maximal 6
Ideal, minimal 50
Ideal, modular 5
Ideal, module isomorphism of right ideals 51
Ideal, nil 8
Ideal, one-sided, in primitive ring with minimal right ideals 90—92
Ideal, order of an element 3
Idempotent elements properties of 48—52
Idempotent elements properties of, central 209
Idempotent elements properties of, completely primitive 59
Idempotent elements properties of, existence of 55 57
Idempotent elements properties of, modulo the radical 53—55
Idempotent elements properties of, orthogonality 49
INDEX 122 135
Index, ring 210
Infinite outer Galois theory for division rings 165—169
Isomorphism theorems for ring of linear transformations 45
Isomorphism theorems for ring of linear transformations for primary rings 59
Isomorphism theorems for ring of linear transformations for primitive ring with minimal right ideals 79
Jordan ring 200
Kronecker product of modules 96
Kronecker product of modules of algebras 102
Kronecker product of modules of algebras of linear transformations 104—107
Kronecker product of modules of distinguished algebras of endomorphisms 132—134
Kronecker product of modules of modules over commutative rings 101
Kronecker product of modules of two-sided modules 99—100
Krull — Schmidt theorem 58
Kurosch’s problem 240—244
Levitzki nil radical 197
Levitzki nil radical, iV-group 140 163
Lie nilpotency 229
| Lie ring 85
Lie solvability 229
Linear function 66
Linear transformation of finite rank 74
Linear transformation of finite rank, ideals in ring of 93
Linear transformation of finite rank, rank of 93
Locally nilpotent ring 197
Matrix ring radical of 11
Matrix ring radical of, ideals in 40
Matrix ring radical of, locally matrix ring 237 240
Matrix ring radical of, matrix subrings 237—240 245
Matrix units 52
Maximum condition 198
Minimum condition for right ideals 38
Minimum condition for right ideals for left ideals 42
Minimum polynomial of algebraic element 19
Minimum polynomial of algebraic element, m-sequence 195
Minimum polynomial of algebraic element, m-system 195
Module basic definitions 1—3
Module basic definitions for semi-simple rings with minimum condition 46—47
Module basic definitions of mappings 160
Module basic definitions, completely reducible 47 60—63
Module basic definitions, extension of 83
Module basic definitions, faithful 4
Module basic definitions, irreducibility of two-sided module 17
Module basic definitions, irreducible 4 6—7 24—37
Module basic definitions, irreducible algebra modules 34—35
Module basic definitions, isomorphism of irreducible modules 45
Module basic definitions, kernel of set of modules 4
Module basic definitions, strictly cyclic 5
Module basic definitions, two-sided 17 142—144 169—175
Morse semigroup 198
Multiplication algebra of an algebra 107
Nil radicals definition 193
Nil radicals definition, upper and lower 194
Nil semigroups 198—199 201
Orthogonal complement of a subspace 70
Peirce decompositions 48 50
PI-algebras 222—235
PI-algebras, II-regular ring 210
Primary ring 56
Prime ideal 194
Prime ring 196
Primitive commutative rings 7
Primitive ideal 4
Primitive ideal, topology of set of primitive ideals 203
Primitive ring 4 24—37
Primitive ring, with minimum condition 39
Primitive ring, with non-zero socles 60—94
Product group of modules 95
Quasi-regularity 7
Radical definition 4
Radical definition of polynomial ring 13
Radical definition of related rings 10—13
Radical definition of ring with minimum condition 39
Radical definition, a nil ideal 19—21
Radical definition, characterizations 9—10
Radical definition, under Kronecker multiplication 122—123
Resolvent set 20
Rings of endomorphisms Completely reducible rings of endomorphisms 124—132
SBI-ring 53
Scalar product 80
Schur’s lemma 26
Semi-linear transformation 44
Semi-primary ring 56
Semi-simple ring 4
Semi-simple ring, with minimum condition 40—42
Simple ring 39 108 109 114
Simple ring, characterization of finite dimensional central simple algebras 118
Socle of module 63
Socle of module of ring 64
Socle of module, homogeneous components of 63—64
Spectrum 19
Splitting field 119 122
Standard identities 227
Stone’s theorem 215
Structure space 204
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) 40
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for algebraic algebras of uniform index 245
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for biregular rings 213
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for Kronecker product of division algebras 176—180
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for Kronecker product of irreducible algebras 113
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for Kronecker product of simple algebras 109 114
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for Kronecker products of primitive algebras having minimal one sided ideads 115—116
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for primary ring 56
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for primitive ring with minimal right ideals 75
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for semi-primary ring 56
Structure theorems for semi-simple ring with minimum condition (Wedderburn-Artin theorem) for simple ring with minimal right ideals 88 90
Subdirectly irreducible rings 219
Subfield separable 178
Subfield separable of division ring 180
Teichmueller’s counter example 147
Topology finite topology 29
Topology finite topology of primitive ring with minimal right ideals 94
Topology finite topology of set of primitive ideals 203
Transitivity, k-fold 32
Uniqueness theorem for direct sum decomposition 42
Uniqueness theorem for direct sum decomposition for structure of primary ring 59
Weakly closed system 200
Weakly Galois subring 142
Wedderburn theorem 183
Wedderburn — Artin theorem 40
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