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| Rosenfeld A. — An introduction to algebraic structures |
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| Предметный указатель |
Absorbent element 109 224
Addition modulo m 143
Addition of cardinal numbers 84
Addition of integers 131
Addition of natural numbers 15
Addition of rationals 133
Algebra 228
Algebraic closure 247
Algebraic element 245
Algebraically independent set 249
Algebroid 228
Annihilate 120
Argument 9
Associate of an element 123
Associate over 226
Associate with 225
Automorphism 93
Automorphism, inner 141
Axiom of Choice 10 36
Base 24
Basis 231
Bernstein — Cantor theorem 82
Bigroupoid 205
Binomial theorem 207
Bound, greatest lower (inf) 30
Bound, greatest lower (inf), least upper (sup) 30
Bound, greatest lower (inf), lower 29
Bound, greatest lower (inf), strict 30
Bound, greatest lower (inf), upper 29
Cancellable element 112 224
cardinal number 80
Cardinality 80
Cauchy's theorem 165
Center 152 246
centralizer 152 214
Chain 26
Chain, ascending 32
Chain, descending 32
Characteristic 211
Chinese remainder theorem 144
Class equation 166
Coefficient 208
Commutator 153 212
Commute (with) 151 225
Composite 115
composition 88
Composition of relations 8
Composition series 103
Composition, associative 114
Composition, commutative 114
Composition, external 222
Composition, n-ary 203
Composition, table 89
Composition, unary 222
Composition, unitary 226
Congruence 94 204 223
Congruence class 94
Congruence, supplemented 105
conjugate 152
Conjugate class 152
Contain, be contained in 2 3
Content 220
Coset 138
Degree of a field over a subfield 247
Degree of a polynomial 208
Denominator 133
Difference 15
DIMENSION 36
Disjoint 3 5
Distribute (over) 205 225 226
Divide 23 122
Division 24
Division of rationals 133
Division ring 211
Divisor 23 122
Divisor of zero 210
Domain 210
Domain of a function 8
Element 1
Endomorphism 93
Equality 1 7
EQUIVALENCE 65
Equivalence class 67
Equivalence, supplemented 79
Euclidean algorithm 218
Euler — Fermat theorem 164
EXPONENT 25
Exponentiation of cardinal numbers 87
Exponentiation of natural numbers 25
Factor 23 122
Factor, direct 104
Factorial 25
Field 211
Field of quotients 215
Field, algebraically closed 248
Field, normal over a subfield 262
Field, perfect 257—258
Field, splitting 251
Finite cardinal number 81
Finite dimensional ordered set 37
Finite dimensional vector space 234
Finite division ring, domain 252—255
Finite field 249—251
Finite groupoid 154
Finite semigroup 161
Finite set 21
Finite vector space 235
Finitely generated abelian group 178—181
Finitely generated element of an I-lattice 63
Finitely generated field 246 256—257 259—261
Finitely generated group 156 160—161
Finitely generated groupoid 154
Finitely generated vector space 234
FRACTION 133
Fraction, lowest terms of 133
Function 8
Function, canonical 69
Function, choice 10
Function, constant 9
Function, embedding 9
Function, identity 9
Function, one-to-one 11
Function, onto 11
Function, order preserving 28
Function, polynomial 209
Function, restriction 9
Fundamental Theorem of Arithmetic 127
Fundamental Theorem of Galois Theory 264
Fundamental theorem on abelian groups 178
Gauss' lemma 220
Generate 63
Greater than 17 81
Greatest common divisor 41 127
Greatest element 30
Group 120
Group of quotients 130
Group of type,  190
Group of units 121
Group with operators 227
Group, abelian 120
Group, alternating 169
Group, aperiodic 184
Group, cyclic 157—158
Group, derived 153
Group, divisible 190
Group, factor 137
Group, Galois 262
Group, hamiltonian 198
Group, indecomposable 168
Group, locally cyclic 194
| Group, periodic 184
Group, quaternion 198
Group, simple 167
Group, solvable 176
Group, symmetric 168
Groupoid 90
Groupoid with operators 227
Groupoid, indecomposable 105
Groupoid, trivial 90
Groupoid, underlying 227
Hausdorff's theorem 36
Homomorphism 92 203 224
Homomorphism, canonical 96
Homomorphism, substitution 208
I-lattice 62
I-tuple 74
Ideal 91 214
Ideal, maximal principal 124
Ideal, prime 125
Ideal, principal 120
Idempotent element 90 108
Identity (element) 109 224
Image 8
Image, homomorphic 93
inclusion 2 7
Independent set in a lattice 44
Independent set in a vector space 230
Independent set in an Abelian group 178
Independent set with respect to an I-lattice 64
INDEX 162
Inductive set 35
Infinite cardinal number 81
Infinite order 163
Infinite set 21
INTEGER 131
Integer, negative 131
Integer, nonnegative 15 131
Integer, positive 131
Intersection 3 4
interval 30
Inverse of a relation 7
Inverse of an element 112
Invertible element 112
Irreducible element 124
Isomorphism 92 204
Jordan — Hoelder theorem 53 103
Kernel of a congruence 109
Kernel of a homomorphism 109
Krull — Schmidt theorem 61 145
Lagrange's theorem 162
Lattice 41
Lattice, complete 41
Lattice, distributive 50
Lattice, modular 50
Lattice-finite division ring, domain 273—274
Lattice-finite field 256—257
Lattice-finite group 156 161
Lattice-finite groupoid 154
Lattice-finite ring 272—273
Lattice-finite semigroup 161
Lattice-finite vector space 235
Law 115 226
Law of cancellation 15 23
Law of dichotomy 26
Law of trichotomy 28
Law, general associative 115 226
Law, general commutative 115 226
Law, general distributive 205 226
Laws of exponents 116 137
Least common multiple 41 129
Least element 30
Length 36
Less than 17
Linearly disjoint 259
Lueroth's theorem 258
Matrix 209
Matrix, scalar 210
Maximal element 31
Maximum condition 33
Minimal element 31
Minimum condition 33
Module 228
Module, unitary 228
Moduloid 227
Monogenic division ring, field 244—245 256—259
Monogenic element of an I-lattice 63
Monogenic group 157—158
Monogenic groupoid 154
Monogenic ring 244
Monogenic semigroup 156—157
Monogenic semiring 244
Monogenic vector space 230 234
Monoid 117
Multiple 23 122
Multiplication modulo m 85
Multiplication of cardinal numbers 144
Multiplication of integers 132
Multiplication of natural numbers 23
Multiplication of rational numbers 132 133
n-tuple 18
Natural number 14
Nilpotent element 120
Nilpotent subset 120
Nonnegative integer 15
Normal series 102
Normal subset 98
Normal sugroupoid 101
Number of elements in a set 21
Number, cardinal 80
Number, natural 14
Numerator 133
One-to-one correspondence 11
Order isomorphism 28
Order of a group 162
Order of an element 163
Order relation 26
Order relation for cardinal numbers 81—84
Order relation for integers 131
Order relation for natural numbers 17—18
Order relation for rationals 133
Ordered pair 5
Ordered set 26
p-group 184
Permutation 12
Permutation, even, odd 169
PL-semigroup 129
Polynomial 208
Polynomial, constant 208
Polynomial, cyclotomic 255
Polynomial, in n indeterminates 209
Polynomial, minimal 246
Power series 208
Power, Cartesian 18 75
Power, direct 104
Preimage 10
Preimage, homomorphic 94
Prime division ring, field 243
Prime element of a semigroup 124
Prime group 156 160 163
Prime groupoid 154
Prime natural number 24
Prime ring 242 243
Prime semigroup 158—159
Prime semiring 240—242
Prime vector space 230
Primitive polynomial 220
Primitive root of  264
Primitive set of endomorphisms 238
Product of cardinal numbers 85
Product of natural numbers 23
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