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Borceux F., Janelidze G. — Galois Theories
Borceux F., Janelidze G. — Galois Theories



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Название: Galois Theories

Авторы: Borceux F., Janelidze G.

Аннотация:

E. Galois (1811-1832) would certainly be surprised to see how often his name is mentioned in the mathematical books and articles of the twentieth century, in topics which are so far from his original work.
Since antiquity, mathematicians have been able to solve polynomial equations of degree 1 or 2. Formulae for solving the equations of degree 3 or 4 were found during the sixteenth century. But it was only during the nineteenth century that the problem of equations of higher degree reached a final answer: the impossibility of solving by radicals a general equation of degree at least 5, and some methods for finding some solutions by radicals when these exist. Galois and Abel certainly played a key role in the development of this theory. All these results can be found in almost every book on Galois theory ... and that's the reason why we considered it useless to present them once more in the present book.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 341

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
#      8
$Aut_{K}(L)$      4
$C_{R}$      86
$Desc(\varphi)$      297
$ev_{A}$      242
$Fam(\mathcal{A})$      186
$F^{\mathbb{C}}$      245 294
$G-Set_{f}$      27
$G-Top_{f}$      61
$Gal[\sigma]$      112 125
$Geom(\mathcal{A,B})$      274
$Hom_{K}(A,B)$      21
$H_{2}(R,\mathbb{Z})$      144
$R\circ S$      170
$R^{-1}$      170
$Split_{B}(p)$      208
$Split_{K}(L)$      62
$Split_{K}(L)_{f}$      28
$Split_{R}(\sigma)$      108 122
$Split_{S}(S)$      107 121
$Split_{\alpha}(\sigma)$      258
$Sp_{R}$      86
$U_{b}$      68
$Z_{\mathcal{C}}$      242
$\alpha!$      209
$\chi^{\mathcal{C}}$      104
$\Delta$      170 280
$\Delta_{X}$      170
$\exists_{f}$      273
$\forall_{f}$      273
$\mathbf{\Delta}$      320
$\mathcal{C}$      144
$\mathcal{C}^{\mathbb{C}}$      242
$\mathcal{O}_{b}$      68
$\mathcal{O}_{e}$      77
$\mathcal{O}_{H}$      67
$\mathcal{O}_{I}$      76
$\Omega$-group      329
$\overline{Ab}$      128
$\overline{Gr}$      128
$\overline{\mathcal{C}}/C$      117
$\pi_{1}(X)$      322
$\Sigma\mathcal{M}$      203
$\varepsilon$      144
2-category      288
AB      128
Admissible class      117
Admissible, relatively-adjunction      117
Algebra      15
Algebra, etale      23
Algebra, split      98
Algebra, strongly separable      315
Algebra, universal      329
Algebraic algebra      17
Algebraic element      1 17
Algebraic extension      1
Atomic subobject      280
Bikernel pair      297
Bilimit      291
bool      71
cat      321
Category of families      186
Category, extensive      194
Category, finitely well-complete      149
Category, internal      102 225
Category, internal discrete      246
Category, Mal'tsev      330
Category, simplicial      320
Central extension      134
Central, double-extension      329
Chevalley fundamental group      213
Chinese lemma      19
CLoCo      201
Clopen      51 69
Codiscrete groupoid      321
Cogroupoid      110
Colim      242
Colimit, universal      269
Commutator      128
Commutator, elementary      128
Compact-open topology      323
Compatible family      267
Complex, singular      320
Conjugate elements      3
Connected component      168 193
Connected groupoid      213
Connected object      187 188
Connected space      168 186
Connected subset      168
Connected, locally path space      217
Connected, locally simply space      323
Connected, locally space      197
Connected, open component      186
Connected, path space      217
Connected, semi-locally simply space      324
Connected, simply space      217
Coproduct, disjoint      270
Coproduct, free completion      189
Cov(B)      207
Covering map      205
Covering morphism      207
Covering, localic      295
Covering, trivial map      205
Covering, universal      211
Cross-section      319
CTop      186
CW-complex      321
Decomposition, precategorical      251
Derivative      4
Descent datum      297
Descent, effective      91
Descent, effective structure      254
Descent, Galois      98
Descent, geometric morphism of effective      297
Descent, morphism of Galois      162 211
Descent, relative Galois      118
Descent, relative morphism      118
Diagram fundamental of a functor      316
Differential equation      328
dim[L:K]      1
Discrete opfibration      325
Disjoint coproduct      270
Effective descent      91
Effective descent structure      254
Entourage      170
Epimorphism, split      219
Equivalent germs      319
Equivalent paths      217
Et(B)      319
Etale      200
Etale geometric morphism      296
Etale internal presheaf      296
Etale map      77 197
Etale-presheaf      296
Extension      134
Extension which splits      23
Extension, algebraic      1
Extension, central      134
Extension, double central      329
Extension, Galois      8
Extension, normal      6
Extension, Picard — Vessiot      328
Extension, separable      5
Extension, universal central      135
Extension, weakly universal central      134
Extensive category      194
Factorization system      144
Faithfully flat      93
Fibration      193
Fibration, discrete      325
Filter      65
Filter, proper      65
Filter, ultra      65
Finitely well-complete      149
FixG      8
Flat      93
Fraction groupoid functor      321
Free coproduct completion      189
Froebenius condition      295
Functor essentially surjective on the objects      247
Functor, internal      103
Functor, pseudo      289
Fundamental diagram of a functor      316
G-Prof      56
G-set      27
Galois closed object      210
Galois connection      9
Galois descent      98
Galois extension      8
Galois group      8
Galois groupoid      112 125 212
Galois subextension      36
Galois theorem      9 28 46 62 112 125 258 295
Galois, external theory      323
Galois, morphism of descent      162 211
Galois, topological group      40
Gal[L:K]      8
Gal[L:K]-$Set_{f}$      28
Geometric morphism      274
Geometric morphism of effective descent      297
Geometric morphism, etale      296
Geometric morphism, hyper connected      280
Geometric morphism, open      295 297
Germ      319
GR      127
Groth      289
Grothendieck topos      267
Group, Chevalley fundamental      213
Group, internal      138
Group, perfect      138
Group, Poincare fundamental      213
Groupoid, codiscrete      321
Groupoid, connected      213
Groupoid, fraction functor      321
Groupoid, fundamental      322 325
Groupoid, Galois      112 125 212
Groupoid, internal      103 228
Groupoid, localic      296
Groupoid, open localic      296
Grpd      321
Hopf formula      144
Ideal      1 15 66
Ideal, maximal      66
Ideal, proper      66
Ideal, regular      74
Idempotent      72
Injective, locally      197
Internal category      102 225
Internal discrete category      246
Internal F-presheaf      245 294
Internal functor      103
Internal group      138
Internal groupoid      103 228
Internal natural transformation      103 104 232
Internal precategory      241
Internal presheaf      103 229 242 302
Internal pseudo-precategory      294
K(a)      18
K(l)      2
K-Alg      21
K-homomorphism      4
Lifting problem      217
Lifting property      218
Lifting, path equivalence      219
Lifting, path property      218
Light map      178
Lim      242
Limit, two dimensional      239
LOC      277
Local section      319
Locale      75
Localic covering      296
Localic topos      268
Locally connected space      197
Locally in $\mathcal{M}$      201
Locally injective      197
Locally path connected space      217
LoCo      197
Mal'tsev category      330
Map, light      178
Map, monotone      178
Minimal polynomial      2 17
Modification      243 290
Module, faithfully flat      93
Module, flat      93
Monotone map      178
Morphism of G-Sets      27
Natural transformation, internal      103 104 232
Nearness      173
Nerve      320 321
Normal extension      6
Object, connected      187 188
Object, Galois closed      210
Object, split      162 258
Open geometric morphism      295 297
Open map      295
Opfibration, discrete      325
Path      217
Path connected space      217
Path equivalence lifting      219
Path, locally connected space      217
Path-lifting property      218
Perfect group      138
Picard — Vessiot extension      328
Pierce spectrum      73
Pierce structural space      77
Poincare fundamental group      213
PreCat      242
Precategorical decomposition      251
Precategory, internal      241
Precategory, internal discrete      246
Presheaf      102
Presheaf, etale internal      296
Presheaf, internal      103 229 242 302
Presheaf, separated      267
prof      71
Profinite G-space      56
Profinite space      47 50 51
Progroup      328
Progroupoid      326
PS      244
Pseudo-functor      289
Pseudo-limit      292
Pseudo-natural transformation      290
Pseudo-natural-transformation      290
PsNat      244
Purely inseparable      329
R-alg      80
Reflection, left exact      156
Reflection, semi-left-exact      162
Replete subcategory      150
Ring      73
Section, local      319
Separable      329
Separable closure      98
Separable extension      5
Separable, strongly algebra      315
Separated presheaf      267
Set      90
Sh(B)      319
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