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Lindstrum A.O. — Abstract algebra
Lindstrum A.O. — Abstract algebra



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Название: Abstract algebra

Автор: Lindstrum A.O.

Аннотация:

My aim in writing this book was to present a logical development of
the fundamentals of Abstract Algebra. I have endeavored to avoid
assuming anything not proved prior to its use, and particularly to avoid
illustrative examples from other parts of mathematics and elsewhere.
Such examples are often more confusing to the student than they
are helpful since the student frequently is not acquainted sufficiently
with the other material to appreciate, or in many instances, even to
understand the examples. So far as I can recall at the moment of
writing, I have deviated from this policy in only two instances: in
some exercises giving groups as rotations of the equilateral triangle
and the square, and in taking up briefly; in Chapter 5, the trisection
of the angle. These two instances may very well be omitted without
interfering with the continuity of the development.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 221

Добавлена в каталог: 16.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$V_{R}^{L}(R)$      103
$А^{B}$      110
Abelian group      57
Absolute value of integers      36
Addition of natural numbers      9
Additive exponent      20
Additive group of N      17
Adjacent words      70
Adjunction      138
Algebra      112
Algebra of rational quaternions      115
Algebra, linear associative      112
Algebra, linear nonassociative      112
Algebra, polynomial      117
Algebra, total matric      169
Algebraic element      135
Algebraic field      136
Algebraic systems      100
Algebraic systems, product of      100
Algorithm, division      118
Alternating group      81
Antecedent of a natural number      9
Anti-automorphism      78
Anti-isomorphism      78
Associate      38
Associative algebra      112
Associative law      7
Associative law for mappings      18
Associative law generalized      19
Automorphism inner, of a group      29
Automorphism of a semigroup      29
Automorphism of algebraic systems      101
Automorphism outer, of a group      59
Basis of an Abelian group      94
Basis of an R-module      108
Belongs to      2
Bilateral ideal      128
Binary operation      6
Cancellation law      10
Canonical matrix, classical      198
Canonical matrix, Jordan      196
Cartesian product      5
Cauchy      75
Cayley      79 202
Center of a group      61
Central of a group      61
Characteristic of a field      93 99 143
Characteristic of a ring      93 99
Characteristic polynomial      202
Circular permutation      79
Classical canonical matrix      199
Closed      6 97
Coefficients leading      117
Coefficients of a linear combination      105
Coefficients of a polynomial      117 127
column      see "property without the modifier column"
Common part      3
Commutative group      57
Commutative property      6 7
Commutative ring      95
Companion matrix      196
Compatible      13
Compatible with the structure of a ring      130
Complete set of conjugates      63
Complete set of residue classes modulo m      43
Component      66 103
Composite      6
Composite of a finite sequence of elements      19
Composition external      97
Composition internal      5
Composition series      90
Composition, factors of      90
Composition, table of a semigroup      28
Congruence modulo m      43
Conjugate elements of a group      63
Conjugate elements over a field      145
Conjugate quaternions      115
Conjugate subfields      142
Conjugate subgroups      63
Contained in      2
coordinates      173
Cosets of a group      53
CYCLE      79
Cyclic group      47 73
Cyclic linear transformation      195
Cyclic permutation      79
Cyclic space      193
Cyclic subgroup      49
Cyclotomic extension of a field      153
Cyclotomic field      152
Cyclotomic polynomial      153
Defined everywhere      6
Defining relations      73
Degree of a permutation      78
Degree of a polynomial      117
Degree of an element over a field      136
Degree of one field over another      136
Degree proper      185
Degree reduced      149
Derivative of a polynomial      121
Diagonal matrix      183
Difference ring      131
Dihedral group      62 73
DIMENSION      109
Direct product of groups      66
Direct sum of groups      66
Direct sum of R-modules      104 188
Direct sum of two linear transformation      188
Disjoint cycles      79
Disjoint sets      3
Distributive law      8
Division algorithm      118
Division ring      95
Divisor      37
Divisor elementary      201
Divisor greatest common      38
Divisor of zero      94
Divisor proper      38
Divisorless ideal      131
Domain integral      95
Domain of integrity      95
Eisenstein's theorem      124
Element adjacent      70
Element conjuate, of a group      63
Element conjugate, over a field      145
Element identity      93
Element inseparable      148
Element neutral      22
Element period of      50
Element permutable      95
Element primitive      154
Element primitive, theorem      155
Element regular      94
Element separable      148
Elementary divisor      201
Elementary matrix      177
Elementary operations on a matrix      176
Empty set      3
Empty word      70
Endomorphism of a semigroup      29
Endomorphism of an algebraic system      100
Endomorphism, sum of      89
Equality      2
Equality of mappings      4
equation      see "polynomial"
Equation homogeneous      175
Equation nonhomogeneous      175
Equation pure      160
Equivalence class      26
Equivalence of matrices      176 177
Equivalence relation      26
Essentially unique factorization      41
Euclidean Domain      125
Euler      43 45
Euler totient function      45
Even integers      45
Even permutation      87
Everywhere defined      6
EXPONENT      20 37
Exponent additive      20
Exponent multiplicative      20
Extension algebraic      136
Extension cyclotomic      158
Extension Galois      156
Extension of a mapping      5
Extension of a semigroup      31
Extension pure      160
Extension transcendental      136
External composition      97
F-automorphism      141
F-isomorphism      144
Factor group      57
Factor invariant      201
Factor of composition      90
Factor, prime factor group      90
Factorization, unique      41 42 123
Factors completely      139
Fermat      45
Field      95 153
Field cyclotomic      152
Field finite      153
Field Galois      153
Field inseparable      148
Field normal      146
Field of quotients      97
Field of quotients of polynomials      127
Field of ratvional numbers      97
Field prime      143
Field root      140
Field separable      148
Field splitting      140
Field stem      139
Finite characteristic      94
Finite extension      133
Finite group      23
Finite sequence      19
For each, for every, for all      1
Form, Smith normal      184 196
free      107
Free group      71
Free module      108
Function, polynomial      120
Galois extension      156
Galois field      153
Galois group      157
Galois resolvent      156
Galois theory of fields      156
Gauss' lemma      124
Gaussian semigroup      123
Generator of a group or semigroup      49
Greatest common divisor      38
Group      23 24
Group alternating      81
Group cyclic      49
Group factor      57
Group free      71
Group Galois      157
Group generators      49
Group product      27
Group quotient      57
Group simple      77
Group subgroup      24
Group symmetric      78
Group with operators      98
Hamilton      202
Hoelder      92
Homogeneous equations      175
Homologous      100
Homomorphism of algebraic systems      101
Homomorphism of semigroups      29
Ideal      128
Ideal bilateral      128
Ideal divisorless      131
Ideal maximal      131
Ideal prime      131
Ideal principal      129
Ideal principal, ring      129
Ideal two-sided      128
Identity element      93
Identity mapping      4
Image      3 5
Imbedding of a semigroup      31 33
IMPLY      1
Improper subgroup      46
Indeterminates      117 127
Indexing set      5
Induced law in quotient set      3 1
Induced law in subset      21
Induction, mathematical      9
Inequality of natural numbers      14
Inner automorphism      59
Inseparable element      148
Inseparable field      148
Inseparable polynomial      148
Integers      35
Integers absolute value of      36
Integers negative      36
Integers positive      36
Integral domain      95
Integrity, domain of      95
Internal composition      5
Intersection      3
Invariant element      98
Invariant factor      201
Invariant maximal subgroup      89
Invariant subgroup      56
Invariant subspace      187
Invariants of an Abelian group      84
Invariants, similarity      201
Inverse element      22
Irreducible element      38
Isomorphism of algebraic systems      101
Isomorphism of semigroups      29
JORDAN      90
Jordan canonical matrix      196
Kernel      57
Lagrange      54
Law associative      7 19
Law cancellation      10
Law commutative      7
Law distributive      8
Law induced in quotient set      31
Law induced in subset      21
Law of external composition      97
Law of internal composition      5
Law of trichotomy      11
Leading coefficient      117
Least common multiple      38
Least residues modulo m      43
Left      see "property without adjective left"
Length of a word      70
linear combination      105
Linear dependence      105 107
Linear mapping      165
Linear mapping, matrix of      169
Linear transformation      165
Linear transformation nonderogatory      195
Linear transformation nonsingular      165
Linear transformation relation      111
Logic      1
1 2
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