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Jacobson N. — Lectures in Abstract Algebra, Vol. 1
Jacobson N. — Lectures in Abstract Algebra, Vol. 1

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Название: Lectures in Abstract Algebra, Vol. 1

Автор: Jacobson N.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 217

Добавлена в каталог: 13.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint of a matrix      59
Algebraic element      94 183
Algebraic extension of a field      101
Algebraic integer      181
Algebraically independent elements      105
Alternating group      37
Alternating group, simplicity of      139
Anti-homomorphism      74
Anti-isomorphism      72
Associated primes of an ideal      174 179
Associates      114
Associative law      8 15
Associative law, generalized      20
Automorphism, group of      45
Automorphism, inner      46
Automorphism, of group      45
Automorphism, of module      165
Automorphism, of ring      68
Binary composition      4
Binary composition, non-associative      18
Binomial theorem      52
Boolean algebra      207
Boolean ring      210
Cayley’s Theorem      28
Center of group      46
Center of ring      64
Chain      188
Chain conditions for groups with operators      142 153 154
Chain conditions for lattices      200
Chain conditions for modules      168
Chain, composition      199
Chain, equivalence of      198
Chain, refinement of      197
Characteristic of ring      74
Characteristic subgroup      130
Circle composition      56
Closure (in a semigroup)      25
Cofactor of a matrix      59
Commutative law      8 21
Commutator      132
Commutator group      132
Complement (in a lattice)      205
Composition, binary      4
Composition, non-associative      18
Composition, ternary      18
Conjugate classes      47
Coset      37
Cover (in a lattice)      188
Decomposable element (in a lattice)      204
Difference ring      66
Dimensionality relation (in modular lattices)      200
Direct product, complete      160
Direct product, of groups with operators      144
Direct product, of invariant subgroups      147
Direct sum      145
Directly projective elements (of a lattice)      204
Distributive law      8
Division ring      54
Divisor (factor)      13 114
Divisor (factor) of ideal      173
Eisenstein’s irreducibility criterion      127
Endomorphism, normal      150
Endomorphism, of group      45
Endomorphism, of module      165
Endomorphism,, radical of      155
Endomorphism,, ring of      80
Endomorphism,, sum of      151
Equivalence classes      5
Equivalence relation      4
Euler $\phi$-function      34 67 121
Euler - Fermat theorem      67
Extension of a field      100
Extension of a ring      84
Factor, see Divisor Factor group      41 131
Field      54 183
Field of fractions      88
Field of subsets      207
Field, extension of      100
Field, prime      103
Field, structure of      103
Fitting’s Lemma      155
Fractions      88
Gauss’ Lemma      125
Greatest common divisor      13 118
Greatest common divisor of ideals      173
Group      23
Group of automorphisms      45
Group with operators      128
Group with operators, decomposable      152
Group with operators, determined by a ring      130
Group with operators, direct product of      145
Group with operators, factor group of      131
Group with operators, homogeneous      158
Group with operators, maximal invariant subgroup      140
Group with operators, subgroups of ($M$-subgroups)      130
Group, cyclic      30
Group, generators of      31
Group, multiplication of      29
Group, regular realizations of      29
Group, simple      139
Group, solvable      139
Hilbert basis theorem      171
Holomorph of group      47
Homomorphism of groups      41
Homomorphism of groups with operators      131
Homomorphism of groups, fundamental theorem for groups with operators      133
Homomorphism of groups, fundamental theorem of      44
Homomorphism of groups, kernel of      43
Homomorphism of groups, natural      43
Homomorphism of lattices      192
Homomorphism of modules      165
Homomorphism of rings      68
Homomorphism of rings, fundamental theorem of      70
Homomorphism of rings, kernel of      69
Ideal      65
Ideal, associated prime      174
Ideal, in a lattice      201
Ideal, left      77
Ideal, primary      174
Ideal, prime      173
Ideal, principal      77
Ideal, radical of      173
Ideal, reducible      175
Ideal, regular      167
Ideal, right      77
Idempotent element      24
Identity element      22
Identity element of lattice      192
Imbedding of commutative inte-gral domain in a field      87
Imbedding of ring in ring with an identity      84
Independence in lattices      202
Induction      7 9
Integers      10
Integers, gaussian      123
Integers, in quadratic fields      184 186
Integral dependence      181
Integral domain      53
Integral domain, Euclidean      122 186
Integral domain, Gaussian      115 184
Integral domain, principal ideal      121
Integrally closed      183 184
Intervals (quotients) in a lattice      192
Intervals (quotients), projective      196
Intervals (quotients), transpose      196
Inverse      22
Irreducible (prime) integer      67
Irreducible element      115
Irreducible element of a lattice      201
Irreducible polynomial      101
Irredundant intersection, of elements of a lattice      201
Irredundant intersection, of elements of a lattice of ideals      177
Isolated components (of an ideal)      180
Isomorphism theorems for groups with operators      135
Isomorphism, of groups      26
Isomorphism, of lattices      192
Isomorphism, of modules      165
Isomorphism, of rings      68
Jordan - H$\ddot{o}$lder theorem      141
Jordan - H$\ddot{o}$lder theorem for lattices      199
Krull - Schmidt theorem      156
Kurosch - Ore theorem      204
Lagrange’s Theorem      39
Lattice      189
Lattice principle of duality in      190
Lattice principle of duality in, semi-modular      197
Lattice, complemented      205
Lattice, complete      189
Lattice, composition series in      199
Lattice, distributive      193
Lattice, modular      194
Least common multiple      14 120
Least common multiple of ideals      173
Leibniz’s theorem      100
Length of element of a Gaussian semi-group      116
Length of element of a lattice      199
Linearly ordered set (chain)      188
M$\ddot{o}$bius function      120
Mapping      3
Mapping, graph of      3
Mapping, induced by an equivalence relation      6
Mapping, inverse      4
Mapping, inverse image of      6
Mapping, order preserving      192
Mapping, resultant of      4
Matrix      56
Matrix, adjoint      59
Matrix, cofactor of      59
Matrix, determinant of      58
Matrix, diagonal      64
Matrix, ring      56
Matrix, scalar      64
Matrix, transposed      72
Maximum condition      169 (see also Chain conditions)
Minimum condition      169
Module      162 163
Module, annihilator      165
Module, cyclic      166
Module, difference      165
Module, generators of      166
Module, modules of a ring      164
Module, quotient      165
Module, unitary      167
Newton’s identities      110
Nilpotent element      55
Order of an element of a group      32
Order of an element of a module      165
Order of semi-group      17
Partially ordered set      187
Peano’s axioms      7
permutations      27
Permutations, decomposition into cycles      34
Permutations, even and odd      36
Poincar$\acute{e}$’s theorem      40
Point (in a lattice)      205
Polynomials      93 97
Polynomials, cyclotomic      127
Polynomials, homogeneous      108
Polynomials, in several elements      105
Polynomials, irreducible      101
Polynomials, polynomial functions      111
Polynomials, primitive      124
Polynomials, symmetric      107
Power series      95
Powers      21
Prime element      14 116
Projection      150
Projection, primitive      158
Quadratic extensions of rational field      184
Quasi-regular      55
Quaternions      60
Quaternions, norm of      63
Quaternions, trace of      63
Quotient group      see Factor group
Quotient in a lattice      192
Quotient of submodules      165
Radical of ideal      173 175
Realization of a group      28 30
Relation      4
Relation, asymmetry of      9
Relation, reflexivity of      5
Relation, symmetry of      5
Relation, transitivity of      5
Ring      49
Ring, additive group of      50
Ring, boolean      210
Ring, commutative      53
Ring, extension of      84
Ring, group of units of      54
Ring, identity of      53
Ring, multiplications of      82
Ring, multiplicative semi-group of      50
Ring, Noetherian      172
Ring, of formal power series      95
Ring, of polynomials      92
Ring, right annihilator of      82
Ring, simple      70
Schreier’s refinement theorem      138
Schreier’s refinement theorem for lattices      198
Semi-group      15
Semi-group, Gaussian      115
Semi-group, group of units of      25
Semi-group, multiplication table of      17
Semi-group, ring      95
Series, characteristic      143
Series, characteristic, chief      143
Series, characteristic, composition      140 143 199
Series, characteristic, fully invariant      130
Series, characteristic, normal      138
Sets      2
Sets, intersection of      2
Sets, logical sum of      2
Sets, product set      3
Sets, quotient set      5
Stone’s theorem      211
Subdirect product (of groups)      160
Subfield      87
Subgroup      24
Subgroup, characteristic      130
Subgroup, cosets of      37
Subgroup, fully invariant      130
Subgroup, generated by a subset      30
Subgroup, index of      39
Subgroup, invariant (normal)      40
Subgroup, left cosets of      39
Subgroup, products of subgroups      76
Sublattice      191
Submodule      164
Subring      61
Subring, division      63
Subring, generated by a subset      63
Symmetric difference      209
Symmetric group      27
Transcendental element      93
Transcendental extension of a field      101
Transformation group      27
Transformation group, transitive      37
Transformations      4
Transitivity set      37
transpositions      36
Uniqueness of factorization in semigroups      117
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