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| Beachy J.A. — Abstract Algebra II |
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| Предметный указатель |
Action, linear 39
Adjoint, of a matrix xiii
Algebra, division 100
Algebra, finite dimensional 99
Algebra, over a field 99
Algebraically closed field 137
Annihilates, of an element 14
Annihilator, of a module 56
Artin 100
Artinian module 67
Artinian ring 67
Ascending central series 31
Associated prime ideal 133
Automorphism, of a ring 15
Basis, for a module 52
Bicommutator, of a module 104
Bilinear function 83
Bimodule 89
Boolean ring 9
Center, of a ring 9
Central series, ascending 31
Chain xiv
Closure, integral 126
Coefficient, leading 3
Cofactor, of a matrix xiii
Completely prime ideal 12 100
Completely reducible module 64
Composition series, for a module 70
Cyclic module 51
Cyclic submodule 51
Dedekind 119
Dedekind domain 120
Degree, of a polynomial 3
Dense subring 114
Determinant xii
Differential operators 4
Dimension, Krull 137
Direct product, of modules 60
Direct sum, of modules 60
Direct sum, of rings 6
Divisible module 83
Division algebra 100
Division ring 8
Divisor of zero 7
Domain 13
Domain, Dedekind 120
Domain, Euclidean 14
Domain, noncommutative 100
Element, idempotent 62
Element, integral 125
Element, invertible 7
Element, maximal xiv
Element, nilpotent 15
Element, regular 7 13
Element, torsion 94
Essential submodule 106
Euclidean Domain 14
Extension, integral 125
Factor ring 12
Faithful module 56
Field xi
Field of fractions 25
Field of quotients 25
Field, algebraically closed 137
Field, of rational functions 26
Finite length 72
Finitely generated module 51
Fitting's lemma 73
Fractional ideal 120
Frattini's argument 33
Free module 52
Frobenius 100
Function, bilinear 83
Generating set 51
Going down theorem 129
Going up theorem 128
Group ring 5 80
Group, nilpotent 31
Hamilton 9 99
hilbert 138
Hilbert basis theorem 68
Holomorph 36 38
Homogeneous component 106
Homomorphism, of rings 15
Homomorphism, split 63
Ideal 10
Ideal, completely prime 12 100
Ideal, fractional 120
Ideal, irreducible 132
Ideal, left 10 50
Ideal, maximal 12 13
Ideal, nil 110
Ideal, primary 132
Ideal, prime 12 101
Ideal, primitive 101
Ideal, principal 10
Ideal, right 10 50
Ideal, semiprime 101
Ideal, two-sided 10
Idempotent element 62
Idempotents, orthogonal 62
Incomparability theorem 128
Indecomposable module 73
Injective module 78
Integral closure 126
Integral domain xi
Integral element 125
Integral extension ring 125
Integrally closed 126
Invertible element 7
Invertible fractional ideal 120
Irreducible ideal 132
Isomorphism 53
Isomorphism, of rings 15
Jacobson density theorem 114
Jacobson radical 106
Jordan — Holder 71
Kernel, of a ring homomorphism 16
Kernel, of an R-homomorphism 53
Kruii 137
Krull 137
Krull dimension 137
Lasker 119
Leading coefficient 3
Left ideal 10 50
Left ideal, maximal 55
Lemma, of Fitting 73
Lemma, of Nakayama 108
Lemma, of Schur 57
Lemma, of Zorn xiv
Length, of a module 72
Linear action 39
Linear independence 52
Linear ordering xiv
Localization of D at P 27
Localization of R at P 29
Lying over theorem 128
Macauley 119
Maschke's Theorem 80
Matrix unit 11
Maximal element xiv
Maximal ideal 12 13
Maximal left ideal 55
Maximal submodule 55
| Minimal submodule 57
Modular law 54
Module 49
Module, Artinian 67
Module, completely reducible 64
Module, cyclic 51
Module, divisible 83
Module, faithful 56
Module, finitely generated 51
Module, free 52
Module, indecomposable 73
Module, injective 78
Module, irreducible 57
Module, Noetherian 67
Module, nonsingular 117
Module, on the right 49
Module, prime 102
Module, projective 66
Module, semisimple 77
Module, simple 57
Module, singular 117
Module, torsion 69
Module, torsionfree 94
Multiplicative set 28
Nakayama's lemma 108
Nil ideal 110
Nil radical 131
Nilpotent element 15
Nilpotent group 31
Noether 119
Noetherian module 67
Noetherian ring 67
Nonsingular module 117
Nonsingular ring 117
Opposite ring 117
Ordering, linear xiv
Ordering, partial xiv
Orthogonal idempotents 62
Partial ordering xiv
Polynomial ring 3
Power series, ring of 135
Primary ideal 132
Primary submodule 138
Prime ideal 12 101
Prime ideal, associated to Q 133
Prime module 102
Prime radical 131
Prime ring 12 101
Primitive ideal 101
Primitive ring 101
Principal ideal 10
Principal ideal domain 14
Principal ideal theorem 137
Principal ideal theorem, generalized 137
Principal left ideal 10
Product, semidirect 34 37
Projective module 66
Quaternions 8
R-automorphism 53
R-bilinear function 83
R-endomorphism 53
R-endomorphism ring 53
R-homomorphism 52
R-module 49
Radical 107
Radical, Jacobson 106
Radical, nil 131
Radical, of an ideal 132
Radical, prime 131
Rank, of a module 93
Rational function field 26
Regular element 7 13
Regular ring 115
Right ideal 10 50
Right R-module 49
Ring ix
Ring automorphism 15
Ring homomorphism 15
Ring isomorphism 15
Ring, Artinian 67
Ring, boolean 9
Ring, commutative x
Ring, group 5
Ring, group ring 80
Ring, Noetherian 67
Ring, nonsingular 117
Ring, of differential operators 4
Ring, of polynomials 3
Ring, of power series 135
Ring, opposite 117
Ring, prime 12 101
Ring, primitive 101
Ring, semiprime 101
Ring, semiprimitive 110
Ring, semisimple Artinian 113
Ring, simple 101
Ring, von Neumann regular 115
Schreier 71
Schur's lemma 57
Semidirect product 34 37
Semiprime ideal 101
Semiprime ring 101
Semiprimitive ring 110
Semisimple Artinian ring 113
Semisimple module 77
Set, multiplicative 28
Simple module 57
Simple ring 101
Singular module 117
Singular submodule 117
Small submodule 106
Socle 77
Split homomorphism 63
Submodule 50
Submodule, cyclic 51
Submodule, essential 106
Submodule, maximal 55
Submodule, minimal 57
Submodule, primary 138
Submodule, singular 117
Submodule, small 106
Submodule, superfluous 106
Subring x 6
Subring, dense 114
Superfluous submodule 106
Tensor product 84
Theorem, generalized principal ideal 137
Theorem, going down 129
Theorem, going up 128
Theorem, incomparability 128
Theorem, Jacobson density 114
Theorem, lying over 128
Theorem, of Maschke 80
Theorem, principal ideal 137
Torsion element 94
Torsion module 69
Torsionfree module 94
Two-sided ideal 10
Unit element 7
Vector space xv
von Neumann regular ring 115
Wedderburn 100
Well-ordered set xiv
Zero divisor 7
Zorn's lemma xiv
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