Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета   Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум    Авторизация         Поиск по указателям Jacobson N. — Lectures in Abstract Algebra, Vol. 3 Обсудите книгу на научном форуме Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter Название: Lectures in Abstract Algebra, Vol. 3 Автор: Jacobson N. Язык: 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 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 Реклама        © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024 | | О проекте