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Lorenz F., Levy S. — Algebra, Volume I: Fields and Galois Theory
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Название: Algebra, Volume I: Fields and Galois TheoryАвторы: Lorenz F., Levy S. Аннотация: From Math Reviews: "This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. Thus, for instance, the transformation of the classical geometrical problems on constructions with ruler and compass in their algebraic setting in the first chapter introduces the reader spontaneously to such fundamental algebraic notions as field extension, the degree of an extension, etc... The book ends with an appendix containing exercises and notes on the previous parts of the book. However, brief historical comments and suggestions for further reading are also scattered through the text."
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1st editionГод издания: 2005Количество страниц: 309Добавлена в каталог: 01.06.2008Операции: Положить на полку |
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Localization at prime ideal 237 Lorenz, Falko 113 259 263 Luroth, Jakob (1844—1910) 240 247 280 Lutkebohmert, Werner ii Malle, Gunther 202 Matsumura, Hideyuki (1930— ) 225 Matzat, B. Heinrich (1945— ) 202 Maximal element 63 Maximal ideal 41 241 Mersenne, Marin (1588—1648) 105 258 Metacyclic see “Solvable” Miller, George Abraham (1863—1951) 255 Minimal polynomial 17 31 Mobius function, inversion formula 264 Mobius, August Ferdinand (1790—1868) 264 Module over a ring (or field) 62 192 Monoid algebra 60 Multiplicative function 237 264 Multiplicative group 24 Multiplicative group of finite field 83 Multiplicative map 62 152 Multiplicative subset 235 237 242 272 n-th roots 143 Nastold, Hans-Joachim (1929—2004) ii 281 Neukirch, Jurgen (1937—1997) 113 Newton, Sir Isaac (1643—1727) 271 Newton’s Formulas 271 Nilpotent group 101 256 Nilradical 218 237 Noether, Emmy (1882—1935) 201 263 Noether, Emmy (1882—1935), isomorphism theorem for groups 170 Noether, Emmy (1882—1935), Noether normalization theorem 214 Noetherian ring 221 Norm 133 Normal basis 120 122 262 Normal closure 60 76 Normal field extension 59 76 Normal series 268 Normal subgroup 24 77 253—254 Normalized polynomial 16 normalizer 98 Nullstellensatz 219 281 Number theory 113 264 Opolka, Hans 105 Orbit 94 Orbit, formula 96 Order of a group element 85 Ordered set 63 p-component 155 p-group 97 154 p-subgroup 99 Pairing 150 Parity see “Signature” Pentagon, regular 1 9 Perfect field 73 Permutation 75 178—182 Permutation, cycle decomposition 179 Polygon, regular 1 3 9 51 104 258 Polynomial algebra 210 Polynomial ring 63 Prime element 37 Prime factorization 39 45 Prime field 31 Prime ideal 41 Prime numbers 39 Prime polynomial 26 Prime residue classes 88 250 Primitive element 21 Primitive element, theorem 78 244 Primitive polynomial 48 Primitive root 86 Primitive root of unity 88 Principal ideal 25 34 41 Principal series 268 Product of ideals 42 43 Product tensor 61 Projective linear group 247 Projective system, projective limit 126 Pure equation 143 Purely inseparable 71 246 Purely transcendental 213 Pythagorean field 263 Pythagorean triple 279 Quadratic equation 165 Quadratic field 259 Quadratic reciprocity law 107 110 111 258 Quadratically closed field 5 Quadrature of the circle 3 9 15 Quotient 28 Quotient, homomorphism 23 Quotient, ring 23 Radical see also “Solvable by radikals” Radical extension 166 Radical of an ideal 218 Rational functions 29 53 173 190 Rational parametrization of circle 279 Reciprocity law 107 111 264 Reduced ideal 219 Relatively prime 42 43 Remak, Robert (1888—1942) 123 Residue-class ring 23 Resolvent 145 Ring of formal fractions 235 Ring, extension 191 Ring, polynomial 63 Ring, simple 41 Root of unity 88 Ruffini, Paolo (1765—1822) 178 Ruler and compass 1 8 51 103 258 Scharlau, Winfried (1940— ) 105 Schmidt, Otto Juljewitsch (1891—1956) 123 Scholz, Arnold (1904—1942) 178 Schonemann, Theodor 241 Schopohl, Ralf ii Schreier, Otto (1901—1929) 147 268 Schulze-Relau, Hubert ii Schur, Issai (1875—1941) 250 Seidenberg, Abraham (1916—1988) 274 Separable closure 71 Separable degree 66 Separable element 66 Separable polynomial 69 143 Shafarevich, Igor R. (1923— ) 178 260 Signature map 181 269 Simple field extension 21 31 78 Simple group 182 254 Simple ring 41 Size of orbit 94 Solvable by irreducible radicals 171 Solvable by radicals 1 166 Solvable equation of prime degree 187 271 Solvable group 167 173 268 272 Speiser, Andreas (1885—1970) 263 Spektrum Akademischer Verlag i Spencer, Mark ii Splitting field 58 Springer-Verlag ii Square-free integer 50 Stabilizer 96 Steinitz, Ernst (1871—1928) 57 Stevin, Simon (1548—1620) 26 Storch, Uwe 230 Structure theorem for finite abelian groups 160 Substitution homomorphism 21 63 Successive see under “Adjunction” Sum of ideals 43 Swan, Richard G. 201 Sylow group (or p-subgroup) 99 255 Sylow, Ludvig (1832—1918) 99 101 Sylow’s Theorems 100 Symmetric functions 174 177 195 273 Tartaglia, Nicolo (1500—1557) 165 Tensor product 242 Tensor product of K-algebras 61 Theorem see also “Fundamental” Theorem on normal bases 120 122 262 Theorem, 90 of Hilbert 140 263 Theorem, Artin — Schreier 147 Theorem, Bertrand 271 Theorem, Capelli 267 Theorem, Cauchy 101 154 Theorem, Cayley 94 Theorem, Chinese remainder 42 Theorem, Dirichlet 251 Theorem, Euler — Lagrange 95 Theorem, Hermite — Lindemann 207 Theorem, Hilbert’s basis 221 280 281 Theorem, Hilbert’s irreducibility 190 201 Theorem, Kronecker 27 Theorem, Kronecker — Weber 259 Theorem, Lindemann 15 Theorem, Luroth 240 247 280 Theorem, Noether normalization 214 Theorem, Nullstellensatz 219 280 281 Theorem, primitive element 78 244 Theorem, structure of finite abelian groups 160 Theorem, Sylow 100 Theorem, Translation 115 Theorem, Wilson 259 Topological group 127 Torsion group 154 Torsionfree group 162 Totally real 276 Totient function 88 264 Trace 133 Transcendence basis 211 Transcendence degree 213 231 Transcendence of 15 52 203 Transcendental extension 17 Transcendental number 15 Transcendental over K 15 Transitive group action 80 94 Transitivity of algebraicness 19 Transitivity of separability 69 Translation 94 Translation theorem 115 Transposition 181 189 Trisection of the angle 1 2 9 52 Tschebyschev see “Chebyshev” UFD 37 45 195 Universal problem 28 235 Universal property 21 Valuation 36 38 40 47 van der Waerden, Bartel Leendert (1903—1996) 177 Variety 222 Weber, Heinrich (1842—1913) 259 Weierstrass, Karl (1815—1897) 206 Wielandt, Helmut (1910—2001) 255 Wikipedia 64 Willhoft, Oda ii Wilson, John (1741—1793) 259 Witt, Ernst (1911—1991) 149 268 Yui, Noriko 202 Zimmermann, Nadja 264 Zorn, Max August (1906—1993) 64 Zorn’s Lemma 63
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