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| Rosenfeld A. — An introduction to algebraic structures |
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| Предметный указатель |
Product, Cartesian, of an I-tuple of sets 74
Product, Cartesian, of two sets 6
Product, direct 104 204 224
Product, weak direct 146
Projection 78
Quotient algebra 204
Quotient composition 95
Quotient group 137
Quotient groupoid 95
Quotient of elements of a group 130
Quotient of natural numbers 24
Quotient of [U,V] 100
Quotient ring 216
Quotient set 67
Radical 269
Rank in a lattice 46
Rank of a vector space 232—233
Rank of an Abelian group (0-rank, p-rank) 183
Rational function 216 248
Rational number 133
Rational number, modulo 1 133
Rational number, positive 132
Refinement of a chain 39
Refinement of a normal series 102
Refinement of an independent set 48
Refinement, proper 39 48
Relation 6
Relation, antisymmetric 28
Relation, composite 8
Relation, congruence 94 204 223
Relation, empty 7
Relation, equality 7
Relation, equivalence 65
Relation, inclusion 7
Relation, inverse 7
Relation, irreflexive 28
Relation, order 26
Relation, reflexive 26 65
Relation, restriction 7
Relation, strict order 28
Relation, symmetric 65
Relation, total order 26
Relation, transitive 26 65
Relation, trivial 7
Relation, weakly antisymmetric 26
Relative complement 3
Relatively prime 128
Remainder 24
Restriction of a function 9
Restriction of a relation 7
Ring 210
Ring of endomorphisms 210
Ring of endomorphisms, dense 236
Ring of endomorphisms, r-transitive 236
Ring with identity 210
Ring, commutative 210
Ring, division 211
Ring, euclidean 218
Ring, Gaussian 219
Ring, principal 219
Ring, residue 216
Ring, semisimple 269—272
Ring, simple 243 266—268
Ringoid 206
Root 209
Schreier refinement theorem 53 103
Schur's lemma 238
Segment 30
Semigroup 117
Semigroup with identity 117
Semigroup, cancellation 120
Semigroup, commutative 117
Semigroup, Gaussian 126
Semigroup, GCD 127
Semigroup, LCM 129
Semiring 207
| Separable element 257
SEQUENCE 18
Set 1 2
Set of operators 223 227
Set with operators 223
Set, denumerable 25
Set, empty 2
Set, finite 21
Set, inductive 35
Set, infinite 21
Set, ordered 26
Set, underlying 90
Set, well ordered 34
Solvability by radicals 264—266
Straightedge and compass constructions 248
Subalgebra 203
Subfield 214
Subgroup 135
Subgroup, normal 138—143
Subgroup, stable 229
Subgroup, supplemented 149
Subgroupoid 90
Subgroupoid, normal 101
Subgroupoid, subnormal 102
Subgroupoid, supplemented 145
Sublattice 42
Submodule 229
Subring 213
Subring, division 214
Subsemigroup 117
Subsemiring 212
Subset 2
Subset, invariant 74
Subset, normal 98
Subset, proper 3
Subset, stable 90 203 223
subspace 230
Subtractions of integers 131
Subtractions of natural numbers 15
Sum of cardinal numbers 84
Sum of natural numbers 15 19
Sum, direct 146 178
Sum, weak direct 179
Supplement of a congruence 105
Supplement of a supplemented subgroup 149
Supplement of an equivalence 79
Supplemented congruence 105
Supplemented equivalence 79
Supplemented subgroup 149
Supplemented subgroupoid 145
Sylow p-subgroup 166
Sylow's theorem 165
Term constant 208
Term of a sequence 18
Term of a sum 15
Term of an I-tuple 74
Term of an n-tuple 18
Term of an ordered pair 5
Transcendence base 249
Transcendence degree 249
Transcendental element 245
Transposition 169
TYPE 188
union 3 4
UNIT 122
Universal algebra 203
Unrefinable chain 39
Unrefinable independent set 48
Unrefinable normal series 102
Value 9
Vector space 228
Wedderburn — Artin Theorems 266 270
Well ordered set 34
Zassenhaus' lemma 102
Zero-ring 210
Zero-semiring 207
Zorn's lemma 35
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