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Surowski D. — Workbook in higher algebra
Surowski D. — Workbook in higher algebra

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Название: Workbook in higher algebra

Автор: Surowski D.

Язык: en

Рубрика: Математика/Алгебра/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 191

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
A.C.C.      135
Action, imprimitive      26
Action, permutation      7
Action, primitive      26
Action, regular      9
Acts on      5
Adjoint, left      180
Adjoint, right      180
Algebra      170
algebraic      45
Algebraic closure      50
Algebraic integer      95
Algebraic integer domain      96
Algebraic number      45
Algebraically closed      50
Algorithm      87
Alternating      177
Alternating bilinear form      35
Alternating group      23
Ascending chain condition      135
Associates      79
Atomic domain      85
Automorphism      8
Balanced      161
Basis      116
Bilinear form, alternating      35
Bimodule      165
Butterfly lemma      111
Category theory      180
Cauchy’s Theorem      2
Characteristic      21 30 44
Characteristic polynomial      131
Characteristic subgroup      30
Chinese remainder theorem      76
Closed      53
Closure      53
Cofree R-module      143
Comaximal ideals      76
Commutative graded algebra      171
Commutator      30 32
Commutator subgroup      30
Companion matrix      130
Complete flag      15
Composite      47
Composition series      31 136
Compositum      47
Conjugacy class      5
Content of a polynomial      81
Convolution      152
Coordinate mappinga      115
CYCLE      23
Cycle type      24
Cycles, disjoint      23
Cyclic group      3
Cyclic R-module      122
Cyclotomic polynomial      69
d.c.c      135
Dedekind domain      100
Dedekind Independence Lemma      52
Degree of an element      45 174
Degree of an extension      44 45
Degree, an extension      44
Descending chain condition      135
Determinantal rank      126
Differential      119
Dihedral group      4
Direct sum      113
Discrete valuation ring      108
Discriminant      65
Disjoint cycles      23
divides      79
Divisible abelian group      142
Division algorithm      87
Division ring      139
Double transitivity      9
Elementary components      123
Elementary divisors      123
Equivariant mapping      7
Euclidean Domain      87
Exact      33 92
EXPONENT      122
Extension      44
Extension degree      44
Extension, Galois      54
Extension, purely inseparable      58
Extension, separable      58
Extension, simple      45 73
Exterior algebra      175
F-algebra      152
Field extension      44
Finitely generated      84
Finitely generated, submodule      92
Fixed point set      5
Fixed points      5
Flag      15
Flag, type      15
Fractional ideal      104
Fractional ideal, principal fractional ideal      104
Frattini subgroup      36
Free product      42
Free R-module      145
Free, group      38
Free, module      116
Frobenius automorphism      60
Fundamental theorem of algebra      65
Fundamental Theorem of Algebraic Number Theory      102
Fundamental Theorem of Galois Theory      54
Galois extension      54
Galois group      52
General linear group      14
Generalized quaternion group      20
Generator of a group      3
Generators and relations      39
Graded algebra      174
Graded ideal      174
Graded, algebra      171
Graded-commutative      171
Grassmann space      178
Greatest common divisor      79 80
Group action      5
Group action, faithful      5
Group algebra      152
Group of units      79 181
Group ring      152
Heisenberg group      35
Hilbert basis theorem      84
Homogeneous ideal      174
Homogeneous, elements      174
Homomorphism, module      92
Hopkin’s Theorem      158
Ideal class group      104
Idempotent      149
Idempotents, orthogonal      149
Imprimitivity      26
Imprivitively      26
Inclusion-Exclusion Principle      62
Integral domain      75
Integral group ring      181
Integrally closed      96
Internal direct sum      92 94 114
Invariant basis number      117
Invariant basis number (IBN)      117
Invariant factors      123
Invertible ideal      106 142
Involution      4
Irreducible      79 136
Irreducible R-module      149
Irreducible, R-module      136
Jacobson radical      155
Jordan canonical form      132
Jordan — Holder theorem      31
k-transitively      27
Kernel of the action      5
Kronecker product      166
Krull topology      64
Lagrange’s Theorem      1
Least common multiple      79 80
Left adjoint      180
Left Artinian      157
Left Noetherian      157
Local ring      138
localization      107
Lower central series      32
Maximal ideal      75
Minimal polynomial      45
Minimal polynomial of a linear transformation      129
Minor      126
Modular law      93 111
Module      91
Module homomorphism      92
Monomorphism      181
Nakayama’s Lemma      157
Near field      63
Nil ideal      156
Nilpotent element      78
Nilpotent, element      156
Nilpotent, group      32
Nilpotent, ideal      156
Noether Isomorphism Theorem      111
Noetherian module      135
Noetherian, module      93
Noetherian, ring      84
Norm map      61
Normal closure      39
Normal series      31
Orbit      5
Orbit-Stabilizer Reciprocity Theorem      5
Order      2 121
Order, infinite      2
Overring      107
p-group      6
p-part      12
Perfect      59
Permutation isomorphic      7
Plucker embedding      178
Pointwise      152
Polynomial, separable      58
Primary decomposition theorem      132
Primary ideal      77
Prime, element      79
Prime, ideal      75
primitive      26
Primitive element      73
Primitive Element Theorem      73
Primitive polynomial      81
Principal ideal      76
Principal ideal domain      84
Prinicpal fractional ideal      104
Projection mappings      115
Projective      141
Projective general linear group      14
Projective space      15 178
Projective special linear group      14
Purely inseparable      58
Purely inseparable, element      58
Quadratic integer domains      96
Quasi-dihedral group      20
Quaternion group      20
Quaternion group, generalized      20
Rank      117
Rational canonical form      130
Regular action      9
Regular normal subgroup      28
Relations      39
Relations matrix      125
Relatively prime ideals      76
Representation      152
Residual quotient      77
Right adjoint      180
Right Artinian      157
Right Noetherian      157
Root tower      72
Schreier refinement theorem      136
Second isomorphism theorem      111
Semi-direct product      17
Semi-direct product, external      18
Semi-direct product, internal      17
Semidihedral group      20
Semisimple      133
Semisimple, linear transformation      139
Semisimple, R-module      148
Semisimple, ring      157
Separable      58 73
Separable element      58
Separable extension      58 73
Separable polynomial      58
Separable, element      73
Short exact sequence      92
Short exact sequence, splitting      118
Short exact sequence, splitting of      95
SIMPLE      136
Simple field extension      45
Simple R-module      136
Simple radical extension      72
Simple ring      150
Smith equivalent      125
solvable      31
Solvable by radicals      72
Solvable group      31
Special linear group      14
Split short exact sequence      118
Splits      95
Splitting field      46 49
Stabilizer      5
Stable      54
Subgroup, characteristic      21 30
Submultiplicative algorithm      87
Subnormal series      31
Sylow subgroup      12
Symmetric algebra      174
Symmetric group      3
System of imprimitivity      26
System of imprimitivity, non-trivial      26
System of imprimitivity, trivial      26
Tensor algebra      173
Tensor product      161
Third isomorphism theorem      111
Torsion element      121
Torsion submodule      121
Torsion-free      121
Totally discontinuous      64
Transitive      7
Transposition      23
U.F.D.      79
Unique factorization domain      79
UNIT      79
Valuation ring      108
Word problem      40
Zassenhaus lemma      111
Zero-divisor      75
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