Bourbaki N. — Algebra I: Chapters 1-3 :: Электронная библиотека попечительского совета мехмата МГУ

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Bourbaki N. — Algebra I: Chapters 1-3

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Название: Algebra I: Chapters 1-3

Автор: Bourbaki N.

Аннотация:

This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Algèbre'. It gives a thorough exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, especially with respect to the tensor product and duality constructions. The third chapter investigates algebras, in particular tensor algebras. Determinants, norms, traces and derivations are also studied.

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Рубрика: Математика/

Серия: Н.Бурбаки. Элементы математики

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Год издания: 1998

Количество страниц: 740

Добавлена в каталог: 04.07.2008

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-structure on a vector K-space      II § no.
-structure, induced      II § no.
-structure, product      II § no.
$\epsilon$ -derivation of a graded algebra, $\epsilon$ -derivation of a ring      III § no.
$\epsilon$ -derivation, inner      III § no.
$\Gamma$ -morphism ( $\Gamma$ a set of operators)      I § no.
$\phi$ -homomorphism      I § no.
$\phi$ -morphism ( $\phi$ a homomorphism of one monoid of operators into another)      I §5 no.
$\phi$ -morphism ( $\phi$ a mapping of one set of operators into another)      I § no.
(K, $\epsilon$ )-derivation of degree $\delta$ , $\epsilon$ -derivation of degree      III §10 no.
Abelian group      I § no.
Absolute value of a rational number      I § no.
Action of one set on another      I § no.
Action, canonical      I § no.
Action, distributive      I § no.
Action, induced      I § no.
Action, quotient      I § no.
Action, right, left, derived from a law of composition      I § no.
Actions which commute      I § no.
Addition      I § no.
Addition of rational integers      I § no.
Additively (law written)      I § no.
Adjoint of a matrix      III § Exercise
Adjunction of a unit element (algebra derived by)      III § no.
Affine function      II § no.
Affine group      II § no.
Affine line, plane, hyperplane      II § no.
Affine mapping      II § no.
Affine space      II § no.
Affine subset, linear variety      II § no.
Affinely free, affinely related family      II § no.
Affinely independent points      II § no.
Algebra derived from an algebra by the adjunction of a unit element      III § no.
Algebra generated by generators subject to relations      III § no.
Algebra obtained by extension of scalars      III § no.
Algebra obtained by restriction of scalars      III § no.
Algebra of a group, of a magma, of a monoid      III § no.
Algebra of dual numbers      III § no.
Algebra of formal power series      III § no.
Algebra of Hamiltonian quaternions      III §2 no.
Algebra of octonians of type ( $\alpha$ , $\beta$ , $\gamma$ , $\delta$ )      III Appendix no.
Algebra of quaternions      III § no.
Algebra of quaternions of type ( $\alpha$ , $\beta$ , ), of type ( $\alpha$ , $\gamma$ )      III § no.
Algebra, A-Algebra      III § no.
Algebra, alternating graded      III § no.
Algebra, alternative      III Appendix no.
Algebra, anticommutative graded      III §4 no.
Algebra, associative      III § no.
Algebra, Cayley      III § no.
Algebra, commutative      III § no.
Algebra, exterior, of a module      III § no.
Algebra, free      III § no.
Algebra, free associative      III § no.
Algebra, free associative and commutative      III § no.
Algebra, free, of a module      III § Exercise
Algebra, graded, over a graded ring      III § no.
Algebra, opposite      III § no.
Algebra, product      III § no.
Algebra, quadratic      III § no.
Algebra, quadratic, of type ( $\alpha$ , $\beta$ )      III § no.
Algebra, quotient      III § no.
Algebra, Rees      III § Exercise
Algebra, restricted, of a monoid      III § no.
Algebra, symmetric, of a module      III § no.
Algebra, tensor, of a module      III § no.
Algebra, total, of a monoid      III §2 no.
Algebra, unital      III § no.
Algebra, universal unital associative, defined by a generating system related by a family of relators      III § no.
Algebra, universal, defined by a generating system related by a family of relators      III §2 no.
Algebra, universal, generated by a set subjected to identities      III § no.
Algebras, linearly disjoint      III § no.
Alternating graded algebra      III § no.
Alternating group      III § no.
Alternating multilinear mapping      III § no.
Alternative algebra      III Appendix no.
Amalgamated sum      I § no.
Annihilated by a scalar (element)      II § no.
Annihilator, left, right      I § no.
Annihilator, of a subset, of an element of a module      II § no.
Antiautomorphism      III § no.
Anticocommutative graded cogcbra      III § no.
Anticocommutative skew graded bigebra      III §11 no.
Anticommutative graded algebra      III § no.
Anticommutative skew graded bigebra      III § no.
Antiderivation, K-antiderivation      III § no.
Antiendomorphism of a ring      II § no.
Associated (B-module) with an A-module and a ring homomorphism A —> A      II § no.
Associated (faithful module) with a module      II § no.
Associated (law of action) with an action      I § no.
Associated (linear mapping) with an affine linear mapping      II § no.
Associated (vector subspace) with a homogeneous element of a symmetric algebra      III § no.
Associated (vector subspace) with a homogeneous element of a tensor algebra      III § no.
Associated (vector subspace) with a homogeneous element of an exterior algebra      III § no.
Associated (vectorspace) with a module over an integral domain      II § no.
Associative algebra      III § no.
Associative algebra, free      III § no.
Associative and commutative algebra, free      III § no.
Associative law      I § no.
Associativity relations in a multiplication table      III § no.
Associativity theorem      I § no.
Associator      III Appendix no.
Attached (affine space) to a vector space      II § no.
Augmentation      III § no.
Automorphism with no fixed point      I § Exercise
Automorphism, inner of a group      I § no.
Automorphism, inner, of a ring      I § no.
Barycentre of m points, barycentre of a family of weighted points      II §9 no.
Barycentric coordinate      II § no.
Bases dual to one another      II § no.
Basic family in a group      I § no.
Basis (M) associated with a basis of M      III § no.
Basis dual of a basis of a module      II § no.
Basis of a module      II § no.
Basis of an algebra      III § no.
Basis of type ( $\alpha$ , $\beta$ ) of a quadratic algebra      III § no.
Basis of type ( $\alpha$ , $\beta$ , $\gamma$ ), of type ( $\alpha$ , $\gamma$ ), of a quaternion algebra      III § no.
Basis, Hamel      II § no.
Basis, projective      II §9 Exercise
Biadditive, Z-bilinear mapping      II § no.
Bicentralizer      I § no.
Bicentralizer of a subalgebra      III § no.
Bicyclic group      I § Exercise
Bidual of a module      II § no.
Bigebra of a monoid      III § no.
Bigebra, anticommutative, anticocommutative, skew graded      III § no.
Bigebra, cocommutative, commutative, graded      III § no.
Bigebra, graded bigebra, skew graded bigebra      III § no.
Bigraded group, ring, module      II § no.
Bigraduation      II § no.
Bilinear mapping      II § no.
Bimodule over algebras      III § no.
Bimodule, (A, B)-bimodule      II § no.
Binomial formula      I § no.
Block product of matrices      II § no.
Boolean ring      I § Exercise
Bordered matrix      II § no.
Bracket, $\epsilon$ -bracket of two derivations      III § no.
C-multilinear mapping      II § no.
Cancellable, left, right, cancellable, element      I §2 no
Cartan — Brauer — Hua Theorem      I § Exercise
Cayley algebra      III § no.
Cayley extension of an algebra      III § no.
Cayley norm, trace      III § no.
Cayley octonians      III Appendix no.
Cayley — Hamilton theorem      III § no.
Central element      I § no.
Central extension      I § no.
Central homothety      II § no.
Central ring homomorphism      II § no.
Central series, lower      I § no.

centralizer      I § no.
Centralizer of a subalgebra of an associative algebra      III § no.
Centralizer of a subset      I § no.
Centralizer of a subset of a field      II § no.
Centralizer subalgebra      III § no.
Centralizing element      I § no.
Centralizing subset      I § no.
Centre      I § no.
Centre of a projective linear mapping      II § no.
Centre of an algebra      III § no.
Change of coordinates, formulae of      II § no.
Characteristic of a field      I § Exercise
Characteristic polynomial of a matrix      III § no.
Characteristic subgroup      I § no.
Class, conjugacy      I § no.
Class, nilpotency, of a group      I § no.
Class, solvability, of a group      I § no.
Coassociative cogebra      III § no.
Cocommutative bigebra      III § no.
Cocommutative cogebra      III § no.
Codiagonal mapping      II § no.
Codimension of a vector subspace      II § no.
Codimension of an affine linear variety      II § no.
Coefficients of a formal power series      III § no.
Coefficients of a linear combination      II § no.
Coefficients of a polynomial      III § no.
Coefficients of a system of linear equations      II § no.
Cofactor of an element of a square matrix      III § no.
Cogebra, A-cogebra      III § no.
Cogebra, anticocommutative graded      III § no.
Cogebra, coassociative      III § no.
Cogebra, cocommutative      III § no.
Cogebra, counital      III § no.
Cogebra, graded      III § no.
Cogebra, opposite      III § no.
Coimage of a linear mapping      II § no.
Coincidence group      I § no.
Cokernel of a linear mapping      II § no.
Column of a matrix      II § no.
Combination, linear      II § no.
Combinations, formal linear (module of)      II § no.
Commutation factor      III § no.
Commutative algebra      III § no.
Commutative field      I §9 no.
Commutative graded bigebra      III § no.
Commutative group with operators      I § no.
Commutative group, free, over X      I § no.
Commutative law      I § no.
Commutative magma      I § no.
Commutative monoid, free, over X      I § no.
Commutative ring      I § no.
Commutativity relations in a multiplication table      III § no 7
Commutativity theorem      I § no.
Commutator group      I § no.
Commutator of two elements      I § no.
Commute, actions which      I § 5 no.
Commute, elements which      I § no.
Compatible (equivalence relation) with a law of composition      I § no 6
Compatible (equivalence relation) with an action      I § no.
Compatible (graduation) with a coproduct      III § no.
Compatible (graduation) with a ring, module, structure      II § no.
Compatible (graduation) with an algebra structure      III § no.
Compatible (mapping) with an action      I § no.
Compatible (mapping) with the operation of a monoid      I § no.
Compatible law of composition and equivalence relation      I § no.
Compatible module or multimodule structure      II § no.
Compatible, left, right (equivalence relation), with a law of composition      I § no.
Complementary minors      III § no.
Component of an element in a direct sum      II § no.
Component of an element with respect to a basis      II § no.
Component submodule of a direct sum      II § no.
Component, homogeneous, of an element in a graded group      II § no.
Component, S-connected      I § Exercise
Composition in M(X)      I § no.
Composition of a family with finite support      I § no.
Composition of an ordered sequence      I § no.
Composition of the empty family      I § no.
Composition of words      I § no.
Composition series      I § no.
Composition, law of      I § no.
Condition, maximal (resp. minimal) (set of subgroups satisfying the)      I § Exercise
Congruence modulo a rational integer      I § no 10
Congruent (elements) modulo an ideal      I § no.
Conjugacy class in a group      I § no.
Conjugate elements in a group      I § no.
Conjugate elements under the operation of a group      I § no.
Conjugate subsets in a group      I § no.
Conjugation, conjugate in a Cayley algebra      III § no.
Conjugation, conjugate in a quadratic algebra      III § no.
Constants of structure of an algebra with respect to a basis      III § no.
Contraction of two indices in a mixed tensor      III § no.
Contragradient of an isomorphism      II § no.
Contragredient of an invertible square matrix      II § no.
Contravariant tensor      III § no.
Coordinate form      II § no.
Coordinate of an element with respect to a basis      II § no.
Coordinate, barycentric      II § no.
Coordinates of a tensor over M with respect to a basis of M      III § no.
Coordinates, homogeneous (system of), of a point in a projective space      II § no.
Coproduct      III § no.
Coset (right, left) modulo a subgroup      I § no.
Cotranspose of an endomorphism      III § no.
Counit      III § no.
Counital cogebra      III § no.
Covariant tensor      III § no.
Cramer formulae, system      III § no.
Cross-ratio      II § Exercise
Crossed homomorphism      I § Exercise
Crossed product      III § Exercise
Cycle of a permutation      I § no.
Cyclic group      I § no.
Decomposable p-vector      III § no.
Decomposition, direct, of a ring      I § no.
Decomposition, reduced decomposition of an element in an amalgamated sum of monoids      I § no.
Defined (group) by generators and relations      I § no.
Defined (monoid) by generators and relations      I § no.
Degree of a homogeneous element in a graded group      II § no.
Degree of a polynomial with respect to the indeterminates such that $j \in J$       III § no.
Degree, total degree, of a monomial      III § no.
Degree, total degree, of a polynomial      III § no.
Degree, total degree, of an element of a free algebra, of a free associative algebra      III § no.
Denominator      I § no.
Derivation of a ring A into a ring A      III § no.
Derivation, K-derivation      III § no.
Derivative, partial      III § no.
Derived (element) from an element of the free algebra by substituting elements for the indeterminates      III § no.
Derived (element) from an element of the free associative algebra by substituting elements for the indeterminates      III § no.
Derived (left action, right action) from a law of composition      I § no.
Derived group of a group      I § no.
Derived series of a group      I § no.
Determinant of a matrix      III § no.
Determinant of a sequence of vectors      III § no.
Determinant of an endomorphism      III § no.
Determinant, Cauchy      III § Exercise
Determinant, Vandermonde      III § no.
Diagonal elements of a square matrix      II § no.
Diagonal matrix of matrices      II § no.
Diagonal of a square matrix, diagonal matrix      II § no.
Diagram, exact      II § no.
Differences, group of      I § no.
Differences, monoid of      I § no.
Differential of an element      III § no.
Dihedral group      I § Exercise
Dilatation      II § Exercise
Dimension of a free module      II § no.
Dimension of a projective space      II § no.
Dimension of a vector space      II § no.
Dimension of an affine linear variety      II § no.
Dimension of an affine space      II § no.
Dimorphism      II § no.

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