Schinzel A. — Polynomials with special regard to reducibility :: Электронная библиотека попечительского совета мехмата МГУ

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Schinzel A. — Polynomials with special regard to reducibility

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Название: Polynomials with special regard to reducibility

Автор: Schinzel A.

Аннотация:

This treatise covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields, and finitely generated fields. The author includes several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields. Some of these results are based on the recent work of E. Bombieri and U. Zannier, presented here by Zannier in an appendix. The book also treats other subjects such as Ritt's theory of composition of polynomials, and properties of the Mahler measure and concludes with a bibliography of over 300 items.

Язык:

Рубрика: Математика/Алгебра/Вычислительная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 558

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

1-form      205
1-form, closed      205
Affine coordinate ring      518
Algebraic point      522
Basis of a lattice      502
Block of a permutation group      495
Block of imprimitivity      495
Blocks conjugate      495
Class $\mathcal{C_0}, \mathcal{C_1}, \mathcal{C_2}, \mathcal{C_3}$       316
Codimension of a variety      518
Coefficient vector of a form      492
Conjecture 1      298
Conjecture 2      443
Content of a polynomial      9
Convex hull of a set      512
Convex set      512
Convex span of points      512
Curve      518
Decompositions equivalent      21
Definition 1      20
Definition 10      88
Definition 11      88
Definition 12      212
Definition 13      223
Definition 14      224
Definition 15      253
Definition 16      260
Definition 17      263
Definition 18      263
Definition 19      271
Definition 2      21
Definition 20      278
Definition 21      298
Definition 22      316
Definition 23      316
Definition 24      316
Definition 25      316
Definition 26      316
Definition 27      390
Definition 28      391
Definition 29      391
Definition 3      24
Definition 30      420
Definition 4      52
Definition 5      58
Definition 6      59
Definition 7      65
Definition 8      88
Definition 9      88
Degree of a permutation group      495
Degree of a variety      519
Denominator of an element of a function field      485
Determinant of a lattice      502
Dickson’s polynomials      24
Dickson’s polynomials of the second kind      162
Differential      205
Differential, closed      205
Dimension of a convex set      512
Dimension of a variety      518
Divisor of a function field      485
Edges of a polytrope      513
Extension, Bauerian      368
Extension, primitive      20
Extreme points      513
Face of a convex set      512
Face of a convex set, exposed      513
Field of rational functions on X      518
Field, arithmetically semi-finite      314
Field, Hilbertian      298 312
Field, Kroneckerian      5 390
Field, separably Hilbertian      314
FORM      10
Form, non-singular      10
Form, singular      10
Frobenius substitution      16
Fundamental domain of a lattice      520
Generalized Bezout theorem      519
Genus of a curve      488
Genus of a function field      485
Height of a polynomial      212
Hensel’s Lemma      484
Hilbert’s irreducibility theorem      4 298 312
Hypersurface      518
Irreducible component of a variety      518
Kernel of a polynomial      278
Kronecker’s substitution      58
Lattice in $\mathbb{R}^n$       502
Lattice in $\mathbb{R}^n$ , full      502
Lattice in $\mathbb{R}^n$ , orthogonal to a given one      521
Lattice in $\mathbb{R}^n$ , primitive      520
Laurent polynomial      88
Laurent polynomial, extreme-monic      253
Leading coefficient of a polynomial      9
Length of a polynomial      212
Local parameter of a prime ideal      481
Mahler’s measure of a polynomial      224
Matrix associated with a polynomial      88
Newton polytope of a polynomial      88
Numerator of an element of a function field      485
Orbit of a permutation group      495
Permutation group, doubly transitive      495
Permutation group, intransitive      495
Permutation group, irnprimitive      495
Permutation group, primitive      495
Permutation group, regular      496
Permutation group, transitive      495
Polynomial, additive      65
Polynomial, bireciprocal      419
Polynomial, complete      59 196
Polynomial, complete indeterminate      201
Polynomial, cyclotomic      263
Polynomial, cyclotomic over a given field      263
Polynomial, extended cyclotomic over a field      263
Polynomial, indecomposable      2 20
Polynomial, integral      59
Polynomial, isobaric      188
Polynomial, monic      9
Polynomial, primary      112
Polynomial, prime      2
Polynomial, primitive      9
Polynomial, reciprocal      391
Polynomial, self-inversive      5 391
Polynomial, tame      52
Polynomial, uniform over an interval      236
Polynomials equivalent      112
Polytope in $\mathbb{R}^n$       513
Prime divisor      481
Prime divisor, totally ramified      482
Prime divisor, unramified      482
Product formula      522
Projective closure of an affine variety      519

Ramification index of a prime divisor      482
Rank of a lattice      502
Residue class in $\mathbb{Z}^r$       316
Residue field degree of a prime divisor      482
Resultant of a system of forms      493
Set arithmetically dense in a residue class      316
Stability subgroup of a permutation group (stabilizer of a letter)      495
Subtorus      520
Supporting hyperplane of a convex set      512
Term extreme      88
Terms opposite      88
Theorem 1      12
Theorem 10      52
Theorem 11      59
Theorem 12      62
Theorem 13      63
Theorem 13'      69
Theorem 14      66
Theorem 14'      70
Theorem 15      71
Theorem 16      72
Theorem 17      75
Theorem 18      89
Theorem 19      92
Theorem 2      13
Theorem 20      92
Theorem 21      96
Theorem 22      101
Theorem 23      104
Theorem 24      110
Theorem 25      122
Theorem 26      160
Theorem 27      161
Theorem 28      165
Theorem 29      168
Theorem 3      15
Theorem 30      187
Theorem 31      196
Theorem 32      201
Theorem 32a      204
Theorem 33      203
Theorem 34      204
Theorem 35      213
Theorem 36      215
Theorem 37      217
Theorem 38      227
Theorem 39      237
Theorem 4      16
Theorem 40      244
Theorem 41      247
Theorem 42      253
Theorem 43      263
Theorem 44      271
Theorem 45      279
Theorem 46      298
Theorem 47      301
Theorem 48      304
Theorem 49      308
Theorem 5      18
Theorem 50      319
Theorem 51      321
Theorem 52      322
Theorem 53      325
Theorem 54      331
Theorem 55      334
Theorem 56      339
Theorem 57      339
Theorem 58      341
Theorem 59      352
Theorem 6      20
Theorem 60      355
Theorem 61      366
Theorem 62      369
Theorem 63      371
Theorem 64      372
Theorem 65      375
Theorem 66      378
Theorem 67      380
Theorem 68      380
Theorem 69      382
Theorem 7      21
Theorem 70      391
Theorem 71      408
Theorem 72      411
Theorem 73      415
Theorem 74      421
Theorem 75      435
Theorem 76      438
Theorem 77      441
Theorem 78      443
Theorem 79      458
Theorem 8      24
Theorem 80      463
Theorem 81      466
Theorem 82      474
Theorem 9      50
Theorem, Bertini      217
Theorem, Bezout (generalized)      519
Theorem, Capelli      92
Theorem, Gauss      498
Theorem, Geyer      70
Theorem, Gordan — Igusa      15
Theorem, Gourin, extended      110
Theorem, Gourin, refined      263
Theorem, Hilbert, refined      298
Theorem, Hilbert, simplified      4
Theorem, Kneser      92
Theorem, Kronecker      59
Theorem, Kronecker — Kneser      62
Theorem, Luroth      13
Theorem, Noether      12 16 201 204
Theorem, Northcott      523
Theorem, Ritt      51
Theorem, Ritt, first      21
Theorem, Ritt, second      24
Theorem, Ruppert      204 213
Theorem, Salomon      215
Theorem, Uchida      313
Theorem, Wojcik      263
Torsion point      521
Variety in affine space      517
Variety in affine space in projective space      519
Variety in affine space, defined over k      518
Variety in affine space, general linear      519
Variety in affine space, pure dimensional      519
Vertices of a polytope      513
Vertices of a polytope, opposite      514
Volume of a lattice      520
Weil height of an algebraic number      522
Weil height, logarithmic Weil height      522
Zariski topology      518

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