Bourbaki N. — Algebra II: Chapters 4-7 :: Электронная библиотека попечительского совета мехмата МГУ

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Bourbaki N. — Algebra II: Chapters 4-7

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Название: Algebra II: Chapters 4-7

Автор: Bourbaki N.

Язык:

Рубрика: Математика/

Серия: Н.Бурбаки. Элементы математики

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 461

Добавлена в каталог: 08.05.2008

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Предметный указатель

$\pi$ -primary component      VII page
$\pi$ -primary module      VII page
Abelian closure      V page
Abelian extension      V page
Absolutely semi-simple endomorphism      VII page
Addition of inequalities      VI page
Adjunction (extension obtained by)      V page
Algebraic closure      V page
Algebraic element in an algebra      V page
Algebraic extension      V page
Algebraic number      V page
Algebraically closed field      V page
Algebraically dependent family, subset      V page
Algebraically disjoint extensions      V page
Algebraically free family of extensions      V page
Algebraically free family, subset      IV page V page
Archimedean ordered group      VI page exercise
Artin — Schreier theorem      VI page
Artin — Schreier theory      V page
Artin’s theorem      V page
Associated elements      VI page
Bezout’s identity      VII page
Budan — Fourier rule      VI page exercise
Characteristic exponent of a field      V page
Characteristic of a ring      V page
Characteristic submodule      VII page exercise
Chinese remainder theorem      VI page exercise
Closed (field, algebraically)      V page
Closed (field, separably)      V page
Closed (relatively algebraically) field      V page
Closed half-line      VI page
Closure (abelian) of a field      V page
Closure (algebraic separable)      V page
Closure (algebraic) of a field      V page
Closure (perfect)      V page
Closure (relative algebraic)      V page
Closure (relative p-radical)      V page
Closure (relative separable algebraic)      V page
Coefficients of a formal power series      IV page
Coefficients of a polynomial      IV page
Compatible (order relation) with a group, monoid structure      VI page
Compatible (order relation) with a ring structure      VI page
Compatible (preorder relation) with a commutative monoid structure      VI page
Complementary orientation      VI page
Composite extension      V page
Composition of series      IV page exercise
Conjugacy class in $\Omega$       V page
Conjugate elements      V page
Conjugate extensions      V page
Constant polynomial, term      IV page
Content      VII page
Coprime elements      VI page
Coproduct in TS(M)      IV page
Cubic extension      V page
Cyclic extension      V page
Cyclic vector space (for u)      VII page
Cyclotomic extension      V page
Cyclotomic polynomial      V page
Decomposable module      VII page
Decomposition algebra (universal) of a polynomial      IV page
Decomposition theorem      VI page
Dedekind’s theorem      V page
Degree (inseparable) of an extension      V page
Degree (separable) of an extension      V page
Degree (total) of a polynomial      IV page
Degree (total) of a rational fraction      IV page
Degree of an algebra over a field      V page
Degree of an algebraic element      V page
Derivation (partial) in a p-radical extension of height =s 1      V page
Derivative (partial) of a formal power series      IV page
Derivative (partial) of a polynomial      IV page
Descartes’rule      VI page exercise
Diagonal, diagonalizable set of endomorphisms      VII page
Diagonalizable, diagonalized algebra      V page
Direct basis      VI page
Direction of a half-line      VI page
Direction vector      VI page
Discriminant of a monic polynomial      IV page
Discriminant of a polynomial      IV page
Discriminant of a sequence of elements      V page
Disjoint (algebraically) extensions      V page
Disjoint (linearly) extensions      V page
Divided power in TS(M)      IV page
Divided power of a series      IV page exercise
Divisibility relation      VI page
Division (euclidean)      IV page
Divisor (greatest common)      IV page VI page
Divisor of an element      VI page
Divisors (elementary) of a module      VII page
Double root      IV page
Eigenspace      VII page
Eigenvalue      VII page
Elementary divisor of a module      VII page
Elementary symmetric polynomial      IV page
Etale algebra      V page
Euclidean Domain      VII page exercise
Euclid’s lemma      VI page
Euler — Lagrange Theorem      VI page
Euler’s identity      VI page IV page exercise
Expansion at the origin of a rational fraction      IV page V page
Exponential of a formal power series      IV page
Exponential type (sequence of)      IV page exercise
Extension (principle of) of algebraic identities      IV page
Extension of a field      V page
Finite extension      V page
Finitely generated extension      V page
Form of degree n      IV page
Formal power series      IV page
Formal power series (generalized)      IV page
Fractions (fields of rational)      IV page
Frobenius homomorphism      V page V page
Galois extension      V page
Galois group of an extension, of a polynomial      V page
Galois theory      V page
Gamma algebra of a module      IV page exercise
Gaussian integer      VII page
Generated (extension)      V page
Generated (Galois extension)      V page
Generated (quasi-Galois extension)      V page
Generating family of an extension      V page
Greatest common divisor (GCD) of elements      VI page
Greatest common divisor of polynomials      IV page
Greatest common divisor of principal ideals      VII page
Half-line (closed, open)      VI page
Half-lines (opposite)      VI page
Hankel determinants      IV page exercise
Height of a p-radical element      V page
Height of a p-radical extension      V page
Height of an element of K(T)      V page exercise
Hermite interpolation formula      IV page exercise
Hermite reduced form      VII page exercise
Homogeneous component of a formal power series      IV page
Imperfect field      V page
Imperfection (degree of)      V page exercise
Indecomposable module      VII page
Indeterminate      IV page
Index of a linear mapping      V page
Indicator (Euler’s)      V page
Indivisible element      VII page
Inflation homomorphism      V page
Inseparable degree      V page
Integral ideal      VI page
Invariant factors of a linear mapping      VII page
Invariant factors of a module      VII page
Invariant factors of a submodule      VII page
Invariants (similarity) of an endomorphism      VII page
Irreducible element      VI page
Irreducible polynomial      IV page
Isobaric polynomial      IV page
Jordan decomposition      VII page

Jordan decomposition (multiplicative)      VII page
Jordan Matrix      VII page
Kummer extension      V page exercise
Kummer theory      V page
Lagrange interpolation formula      IV page
Law (polynomial)      IV page exercise
Leading coefficient      IV page
Least common multiple (LCM) of elements      VI page
Least common multiple of principal ideals      VII page
Lefschetz’s principle      V page
Lexicographic product of ordered groups      VI page
Linear topology      IV page
Linearly disjoint extensions      V page
Linearly topologized algebra      IV page
Logarithm of a formal power series      IV page
Logarithmic derivative      IV page
Luroth’s theorem      V page exercise
Mac Laner’s criterion      V page V page
Maximal ordered field      VI page
Minimal polynomial of an element      V page
Minimal polynomial of an endomorphism      VII page
Minkowski’s lemma      VII page exercise
Monic polynomial      IV page
Monogenous extension      V page
Monomials      IV page
Multiple factor (polynomial without)      IV page
Multiple of an element      VI page
Multiple root      IV page
Multiplicity (geometric) of an eigenvalue      VII page
Multiplicity of a root      IV page
Multiplicity of an elementary divisor      VII page
Negative basis      VI page
Negative element      VI page
Negative n-vector      VI page
Newton polygon      V page exercise
Newton’s relations      IV page IV page
Nilpotent component      VII page
Norm      V page
Normal basis, normal basis theorem      V page
Normal extension      V page
Open half-line      VI page
Opposite half-lines      VI page
Order of a (generalized) formal power series      IV page IV page
Order of a root      IV page
Orderable field      VI page exercise
Ordered extension      VI page
Ordered field      VI page
Ordered group, monoid      VI page
Ordered ring      VI page
Orientation of a vector space      VI page
Oriented affine space, vector space      VI page
p-adic integers (ring of)      V page
p-basis      V page
p-basis (absolute)      V page
p-free family      V page
p-radical closure      V page
p-radical element      V page
p-radical extension      IV page
p-torsion group      VII page
Perfect closure of a ring      V page
Perfect field      V page
Perfect ring of characteristic p      V page
Polynomial function      IV page
Polynomial law      IV page exercise
Polynomial mapping      IV page
Polynomial mapping (homogeneous)      IV page
Polynomial, polynomial algebra      IV page
Positive basis      VI page
Positive element      VI page
Positive n-vector      VI page
Power series (generalized formal)      IV page IV page
Preordered group, monoid      VI page
Primary extension      V page
Prime field, subfield      V page
Primitive element (theorem of the)      V page
Primitive root of unity      V page
Principal fractional ideal      VI page
Principal ideal domain      VII page
Principal ideal ring      VII page exercise
Product (lexicographic) of ordered groups      VI page
Product of ordered groups      VI page
Product orientation      VI page
Puiseux’s theorem      V page exercise
Pure basis      V page
Pure extension      V page
Pure submodule      VII page exercise
Pythagorean field      VI page exercise
Quadratic extension      V page
Quadratic reciprocity (theorem of)      V page exercise
Quasi-Galois extension      V page
Quotient in euclidean division      IV page
Quotient orientation      VI page
Rational fraction      IV page
Rational function      IV page
Reduced ring      V page
Regular algebra      V page
Regular extension      V page
Relative algebraic closure of a field in an extension      V page
Relatively algebraically closed field in an extension field      V page
Relatively prime polynomials      IV page
Remainder in euclidean division      IV page
Representatives (system of) of irreducible elements      VII page
Restriction homomorphism      V page V page
Resultant of two polynomials      IV page
Root of a polynomial      IV page
Root of unity      V page
Rule of signs      VI page
Semi-simple (absolutely) component      VII page
Semi-simple (absolutely) endomorphism      VII page
Semi-simple endomorphism      VII page
Semi-simple module      VII page
Separable algebra      V page
Separable algebraic closure (relative)      V page
Separable algebraic extension      V page
Separable closure      V page
Separable degree      V page
Separable element      V page
Separable extension      V page
Separable polynomial      V page
Separably closed field      V page
Separating transcendence basis      V page
Series on E with values in F      IV page exercise
Set ( $\Gamma$ -)      V page
Sign of an element      VI page
Similar endomorphisms, matrices      VII page
Similarity invariants of on endomorpism      VII page
Simple module      VII page
Simple root      IV page
Splitting field, extension      V page
Subextension      V page
Subfield      V page
Substitutable element in a rational fraction      IV page
Substitution in a formal power series      IV page
Substitution in a polynomial      IV page
Substitution in a rational fraction      IV page
Symmetric (elementary) polynomials      IV page
Symmetric formal power series      IV page
Symmetric polynomial      IV page
Symmetric product of symmetric tensors      IV page
Symmetric rational fraction      IV page
Symmetric tensor      IV page
Symmetrized tensor      IV page
Tangent linear mapping      IV page
Taylor’s formula for formal power series      IV page
Taylor’s formula for polynomials      IV page
Term, constant term, of a formal power series      IV page
Term, constant term, of a polynomial      IV page
Trace      V page
Transcendence basis      V page
Transcendence degree      V page

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