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| Behrens E.-A. — Ring Theory: Volume 44 in Pure and Applied Mathematics |
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| Предметный указатель |
Abelian group 3
Additive mapping 5
Adherent 30
Algebra 19
Algebra, central 129
Algebra, epimorphism 20
Algebra, homomorphism 20
Algebra, isomorphism 20
Algebra, left ideal 55
Algebra, module 54
Algebra, monomorphism 20
Algebra, separable 134
Algebra, splitting field of 131
Algebraic element 98
Algebraically closed 100
All relation 38
Annihilator 263
Arens — Kaplansky Theorem 304
Arithmetic ring 229
Artinian ring 35
Asano order 169
Automorphism 83
Balanced map 108
Basic neighborhood 28 292
Bilinear form 189
Bilinear form, associative 189
Bilinear form, nondegenerate 189
Bimodule 106
Binary operation 1
Biregular ring 286 304
Boolean lattice 91 308
Boolean ring 307
Boolean ring, characterization of 307
Boundary of set 296
Center of ring 19
Central idempotent 284 289
Centralizer of module 11
Centroid 128
Chain 15
Chain, length 117
Chain, refinement of 119
Character module 177
Characteristic function 284
Characteristic of division ring 98
Chinese remainder theorem 230
Closed set 29 291
Closed submodule 265
Closure of set 30
Closure operator 291
Coarser (of relations) 39
Comaximal ideals 73
Compact space 294
Complemented 77 90
Composition series 120
Congruence relation on ring 38
Congruence relation on semigroup 37
Continuous mapping 301
Coprime ideals 228
Coset 39
Dedekindian ring 224
density 25 28 30
Density of subdirect sum 65
Direct sum of subspaces 43
Direct sum, complete of modules 75
Direct sum, complete of rings 63
Direct sum, discrete, of modules 75
Direct summand 77
Discrete topology 31 65 301
Distributive laws, for lattice 34
Distributive, D 216 243
Distributively representable ring 92 218
Divisible group 176
Division ring 9
Domain 96
Domain, quotient field of 96
Dual basis 187
Dual basis with respect to bilinear form 201
Dual of module 186
Dual of statement 33
Embedding 8
Endomorphism 5
Epimorphism 6
Epimorphism, natural 37 39
Equivalence relation 37
Equivalent orders 170
Equivalent refinements 119
Equivalent representations 115
Essential extension 179 252 265
Exact sequence 166
Factor module 39
Field 9 (see also Specific type)
Finer, of relations 39
Finite topology 30
Fitting’s Lemma 163
Free module 160
Frobenius algebra 185 189
Galois field 102
Goldie’s chain conditions 265
Goldie’s Theorem 277
Group 2 (see also Specific type)
Group algebra 199
Groupoid 249
Hausdorff space 293
Homomorphism 6
Homomorphism, kernel of 39
Ideal (s) 23 (see also Specific type)
Ideal (s), independent set 263
Ideal (s), inverse of 170
Ideal (s), primary radical of 227 250
Idempotent (s) 43 (see also Specific types)
Identity 2
Indecomposable module 149
Induced topology 294
Injective huil 181 267
Injective module 175 205
Inner automorphism 137
Integral ideal 169
Inverse mapping 8
Irreducible module 23
Irreducible polynomial 97
Irreducible representation 116
Irredundant 254
Isomorphism 6
Jacobson density theorem 27
Join 33
Join, irreducible 216
Jordan — Holder theorem 117
Kruil — Schmidt theorem 164
L over K, trace of 122
Lattice 33 (see also Specific types)
Lattice antiisomorphism 34
Lattice isomorphism 34
Left ideal 23
Left ideal, minimal 35
Left ideal, modular 51
Left ideal, nilpotent 50 62
Left ideal, quasiregular 60
Left multiplication 8
Linear dependence 13
Linear form 186
| Linear functional 179
Linear independence 13
Linear transformation of finite rank 42
Local ring 156
localization 225
Locally compact space 294
Loewy series 213
Mapping 1 (see also Specific types)
Mapping, k-linear 11
Mapping, product of 1
Mapping, sum of 3
Maschke’s Theorem 207
Matrix representation 114
Matrix, trace of 120
Maximal element 14
Maximal linearly independent set 13
Maximal order 170
Meet 33
Meet, irreducible 250
Minimal condition 35
Minimal module 77
Minimal polynomial 98
Modular lattice 34
Module (see also Specific types)
Module, absolutely irreducible 126
Module, completely reducible 79
Module, component of 149
Module, double centralizer of 84
Module, faithful 10
Module, homogeneous 80
Module, homogeneous component 80
Module, left R 10
Module, right R 10
Module, tensor product of 107
Module, unital 10
Monomorphism 6
Multiplication algebra 128
Multiplication ring 252
Nakayama’s characterization of 199
Nakayama’s Lemma 168 213
Neighborhood 28
Neighborhood basis 28
Nil ideal 62
Nilpotent element 62
Noetherian ring 249
Nonassociative ring 249
Null relation 38
Open cover 293
Open set 29 291
Opposite ring 232
Order, left 170 260
Order, right 170
Ore’s condition 261 277
Orthogonal idempotents 150
Partial order 14
Partial order, antiisomorphism of 33
Polynomial ring 94
Polynomial, degree of 95
Polynomial, normalized 95
Polynomial, splitting field of 99
Primary ideal 227
Prime ideal 67
Prime ring 237 240 264
Primitive element 103
Primitive Element Theorem 104
Primitive ideal 53
Primitive idempotent 151
Primitive ring 28
Principal ideal domain 96
Product topology 65
Projection 42
Projective module 166
Quasi — Frobenius ring 184 192
Quasiregular element 60
Quasiuniserial semigroup 240
Quaternions 142
Quotient ring 169 260
Regular element 169
Relation 14
Relation, antisymmetry of 14
Relation, reflexivity of 14
Relation, transitivity of 14
Representation (see also Specific types)
Representation module 114
Representation of algebra 114
Representation, absolutely irreducible 126
Representation, completely 116
Representation, faithful 22
Representation, first regular 22
Representation, reducible 116
Representation, trace of 120
Right algebra 284
Right ideal 23
Right identity modulo L 51
Ring 4 (see also Specific types)
Ring of fractions 225
Ring with DCC 35
Ring, order in 169
Ring, radical of 58
Ring, structure space of 297
Ring, subdirect sum of 64
Sandwich matrix 239
Schreier refinement theorem 119
Schur’s lemma 24
Self-injective ring 182
Semicomplement 265
Semigroup 1 (see also Specific types)
Semigroup ring 93
Semilinear map 48
Semiperfect ring 152
Semiprime ring 264
Semisimple 58
Separable element 104
Separable field extension 104
Separable polynomial 104
Simple ring 36
Small submodule 168
Socle 193
Submodule 23
Subring 6
Support (of a function) 284
Tensor product, characterization of 108
Tertiary ideal 251 256
Tertiary radical 251
Tn-space 293
Topological ring 29
Topological space 28
Totally disconnected space 293
Transcendental element 98
Uniserial ring 224
UNIT 60 260
Upper bound 14
Vector space 10
Vector space, basis of 14
Vector space, dimension of 14
Wedderbum — Artin theorem 69
Wedderbum’s principal theorem 143
Wedderbum’s theorem 138
Zero divisor 260
Zero-dimensional topological space 296
Zorn’s Lemma 15
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