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Jacobson N. - Lectures in Abstract Algebra, Vol. 3 :: Электронная библиотека попечительского совета мехмата МГУ
 
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Jacobson N. - Lectures in Abstract Algebra, Vol. 3
Jacobson N. - Lectures in Abstract Algebra, Vol. 3

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Название: Lectures in Abstract Algebra, Vol. 3

Автор: Jacobson N.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1980

Количество страниц: 323

Добавлена в каталог: 13.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian extension field      61 Chapter
Abelian p-extensions      132-140
Algebraic closure      142
Algebraic closure, separable      146
Algebraic closure, uniqueness of      145
Algebraic element      6
Algebraic field extension      44
Algebraic field extension, absolutely      147
Algebraic functions      156
Algebraic independence      4 151-157
Algebraic independence of isomorphisms      56
Algebraically closed field      142-147
Algebras      7-9
Algebras of dual numbers      168
Algebras, algebraic      10
Algebras, homomorphism of      7
Algebras, ideals of      7
Algebras, tensor products of      15-17
Artin's theorem on positive definite rational functions      289
Bilinear mapping      10
Bott - Milnor theorem      315
CHARACTER      75
Character group      117
Character group of finite commutative group      116-119
Characteristic polynomial      64
Cohomology groups      82
Complete field (relative to a real valuation)      217
Complete field (relative to a real valuation), finite dimensional extensions of      256-262
Completion of a field (relative to a real valuation)      216-221
Composites of fields      83-89 262-264
Composites of fields, free      203-209
Constant      169 194
Crossed product      79
Cyclic algebra      80
Cyclic extension field      61
Cyclic p-extensions      139-140
Cyclotomic field      95 110-116
Decision method      300-307
Dedekind independence theorem      25
Degree of separability and inseparability      49
Dependence relations      153-155
Dependence relations, algebraic      151-157
Derivations      167-174 183
Derivations, constant relative to      169
Derivations, Galois theory of      185-191
Derivations, higher      191-197
Derivations, iterative higher      196
Different      73
Direct sum      9 85
Discriminant of a polynomial      92
Discriminant of an algebra      66
Equations with symmetric group as Galois group      105-109
Exponential function in p-adic numbers      226-228
Extension of derivations      170-172 174-185
Extension of homomorphisms      2-6 246-248
Extension of valuations      246-250 256-265
Factor set      79
Finite fields      58-62
Finite topology      149
Formally real field      271
Frobenius' Theorem      314
Fundamental Theorem of Galois Theory      41
Fundamental theorem of Galois theory for infinite dimensional extensions (Krull's theorem)      150
Fundamental theorem of Galois theory for purely inseparable extensions of exponent one      186
Galois cohomology      75-83
Galois correspondence      23
Galois correspondence for subgroups and subfields      29
Galois extension field      27
Galois group of an equation      89-97
Galois group of an extension field      27
Galois group of cyclotomic extensions      96 113 115
Galois group of general equation      104
Galois group of quartic equations      94-95
Galois group of simple transcendental extensions      158-159
Galois theory for purely inseparable extensions of exponent one      185-191
Galois' criterion for solvability by radicals      98-102
General equation of n-th degree      102-105
Groups of automorphisms of fields      27-31
Hensel's lemma      230-232
Hilbert nullstellensatz      254
Hilbert's "Satz 90"      76
Hilbert's 17th problem      289
Homomorphism of additive group of a field      19
Homomorphism of an algebra      7
Hopf's theorem      315
Ideal      7
Ideal, imbedding in maximal ideal      255
Ideal, imbedding in prime ideal      253
Ideal, radical of      209 253
Indeterminates      4
Infinite Galois theory      147-151
Integral closure      255-256
Isometric mapping      221
Jacobson - Bourbaki theorem      22
Kronecker product      see "Tensor product"
Kummer extensions      119-124
Lie algebra of linear transformations      174
Lie algebra of linear transformations, restricted      174
Lie commutator      173
Linear disjointness      160-167
Local dimensionality      265
Lueroth's theorem      157-160
MacLane's criterion      164
Minimum polynomial      6
Multiple roots      37
Noether's Equations      75
Norm      65
Norm, transitivity of      66
Normal basis      56 61
Normal closure      43
Normal extension      43 52-53
Number of solutions of quadratic equations in finite fields      62
Order isomorphism      238 271
Ordered field      270
Ordered field, Archimedean      272
Ordered group      237
Ordered group of rank one      244-246
Ordered group, rank of      243
Ostrowski's theorem      260
p-adic numbers      222-230 234-236
p-basis      180
p-independence      180
Perfect closure      146
Perfect field      146
Place      241
Positive definite rational functions      289-295
Power series      233-234
primitive elements      54-55 59
Pure equation      95
Pure transcendental extension      155
Purely inseparable extension      47
Purely inseparable extension, exponent of      179
Purely inseparable extension, Galois theory of      185-191
Ramification index      265
Rationally specializable property      291
Real algebraic numbers      287-289
Real closed field      273
Real closed field, characterization of      276-278 316-318
Real closure      284-286
Representation matrix      63
Representation regular      63
Residue degree      265
Residue field      222
Resultant      298-299
Root tower      98
Roots of unit      95 110-116
Seidenberg's decision method      300-307
Separable algebraic closure      146
Separable element      45
Separable extension      46 166
Separable polynomial      39
Separating transcendency bases      161 164-167
Separating transcendency bases and derivations      178-179 184
Solvable extension field      61
Splitting field of a polynomial      31
Splitting field of a polynomial, isomorphism theorem for      35
Standard sequence      281
Sturm sequence      279
Sturm's theorem      283 295
Sturm's theorem, generalized (Tarski's theorem)      312
Subalgebra      7
Tarski's theorem      312
Tensor products      10-17
Tensor products of algebras      15-17
Tensor products of fields      52 84-87 197-203
Tensor products of subalgebras      16
Tensor products of vector spaces      10-15
Theorem of Abel - Ruffini      104
Theorem of Hilbert - Landau      289
Trace      65
Trace form      66
Trace, transitivity of      66
Transcendency basis      151-157
Transcendency basis, separating      161 164-167
Transcendency degree      155
Transitivity theorem for determinants      68
Unit group in p-adic numbers      225-230
Valuation ring      222 240
Valuations of field of rational numbers      214-216
Valuations of simple transcendental extensions      216
Valuations, archimedean      213
Valuations, discrete      222
Valuations, equivalence of      212
Valuations, general      238
Valuations, p-adic      211
Valuations, real      211
Witt vectors      124-132 234-236
wronskian      185
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