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| McCoy N.H. — Rings and ideals |
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| Предметный указатель |
Abelian group 10
Abstractly identical rings 72
Addition 1
Adjoint 157
Algebra of logic 138
Algebraic manifold 203
Annihilator 159
Ascending chain condition 193
Associative laws 1
Basis of an ideal 58
Boolean algebra 138
Boolean algebra, ring 140
Characteristic 24
Characteristic, ideal 163
Characteristic, polynomial 163
Commutative elements 9
Commutative elements, law 1
Commutative elements, ring 9
Complement 96
Complete direct sum 124
Congruence modulo an ideal 62
Congruence modulo an ideal, modulo an integer 28
Constant term 33 48
Contain 54 100
Degree 33 47 48
Direct sum 114 118
Distributive laws 1
Division ring 19
Division ring, transformation 36
Divisor of zero 14
Equality 27
Equivalence classes 29
Equivalence classes, relation 28
Factor Theorem 40
Field 21
Finite field 23
Fundamental theorem of algebra 86
Galois field 23
Greatest common divisor 42
Homomorphic image 68
Homomorphism 68
Ideal 52
Ideal, generated by an element 55
Ideal, generated by several elements 58
Ideal, of a manifold 203
Image of an element 68
Image of an element, of an ideal 76
Indeterminate 31
Integral domain 15
Intersection of sets 5
Intersection of sets, of ideals 77
Inverse 16
Inverse, image 76
Irreducible ideal 199
Irreducible ideal, manifold 205
Irreducible ideal, polynomial 44
Irredundant representation 184
Isolated component 192
Isolated component, primary component 193
Isomorphic image 70
Isomorphism 70
Jacobson radical 132 133
Kernel 74
Leading coefficient 33
Left factor (divisor) 40
Left factor (divisor), remainder 38
Linear system 101
Manifold 203
Manifold of an ideal 203
Matrix 151 158
Maximal element 100
Maximal element, ideal in a ring 80 100
| Maximal element, prime ideal belonging to an ideal 110
Maximum principle 101
Meet 104
Minimal prime ideal belonging to an ideal 103
Minimum function 163
Monic polynomial 33
Multiplication 1
Multiplicative system 89
Nilpotent element 100
Noetherian ring 196
Noncommutative ring 9
Null ideal 162
One-to-one correspondence 70
p-ring 144
Polynomial 31
Primary ideal 180
Prime ideal 96
Prime ideal, ideal belonging to an ideal 182 190
Principal ideal 55
Product of elements 1
Product of sets 5 139
Proper divisor of zero 14
Quasi-regular element 132
Radical ideal 201
Radical ideal of a ring 124
Radical ideal of an ideal 99
Rank of a matrix 159
Reducible ideal 199
Reducible ideal, manifold 205
Reducible ideal, polynomial 44
Reflexive law 28
Regular ring 147
Related to an ideal 107 108
Remainder theorem 39
Representation as subdirectsum 128
Residue class 64
Residue class, class ring 64
Resultant 171
Right factor (divisor) 40
Right factor (divisor), remainder 38
Ring 1
Ring, of finite subsets 7
Ring, of integers modulo n 3
Ring, of matrices 8 153
Ring, of quotients 88 94
Ring, of real quaternions 8
Ring, of subsets 4 139
Root 40
Scalar matrix 153
Short representation 191
Skew field 19
Solution 202
Subdirect sum 121
Subdirectly irreducible 128
Subdirectly irreducible, reducible 128
Subring 2 52
Subset 4
Sum of elements 1
Sum of ideals 78
Sum of sets 5 139
Symmetry, law of 28
Term 47
Transitive Law 28
Two-sided ideal 53
Union of ideals 77
Union of sets 100
Unit element 15
Unrelated to an ideal 108
Void set 5
Zero element 10 11
Zero element, ideal 53
Zorn's lemma 101
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