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.

Язык:

Рубрика: Математика/

Серия: Н.Бурбаки. Элементы математики

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1998

Количество страниц: 740

Добавлена в каталог: 04.07.2008

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Предметный указатель

Invariant subgroup, stable subgroup      I § no.
Inverse limit      Limit inverse
Inverse system      System inverse
Inverse, left inverse, right inverse, element      I § no.
Inverse, left, right inverse, of a linear mapping      II § no.
Inversion in a bigebra      III § Exercise
Inversion of a permutation      I § no.
Invertible square matrix      II § no.
Invertible, left invertible, right invertible, element      I § no.
Invertible, left, right invertible, linear mapping      II § no.
Irreducible ideal      I § Exercise
Isobaric element      II § no.
Isomorphic magmas      I § no.
Isomorphism, magma      I § no.
Jacobi identity      III § no.
Jordan — Holder theorem      I § no.
Jordan-Holder series      I § no.
Juxtaposition      I § no.
K-differential      III § no.
Kernel of a group homomorphism      I § no.
Kernel of a linear mapping      II § no.
Kronecker symbol      II § no.
Krull's theorem      I § no.
Laplace expansion      III § no.
Law and equivalence relation, compatible      I § no.
Law not everywhere defined      I § no.
Law of composition      I § no.
Law of left, right, operation of a monoid on a set      I § no.
Law of right, left action associated with an action      I § no.
Law written additively, multiplicatively      I § no.
Law, associative      I § no.
Law, commutative      I § no.
Law, group      I § no.
Law, induced      I § no.
Law, left distributive, right distributive, distributive with respect to another      I § nos.
Law, opposite      I § no.
Law, quotient      I § no.
Least common multiple (l.c.m.) of two integers      I § no.
Leibniz formula      III § no.
Lemma, Zassenhaus's      I § no.
Length of a decomposition in an amalgamated sum      I § no.
Length of a group      I § no.
Length of a module      II § no.
Length of a word      I § no.
Length of an element in a free group      I § Exercise
Length of an element in a free magma      I § no.
Limit, direct, of $A_\alpha$ -algebras      III § no.
Limit, direct, of $A_\alpha$ -modules      II §6 no.
Limit, direct, of actions      I § no.
Limit, direct, of graded algebras      III § no.
Limit, direct, of groups, of groups with operators, of monoids      I § no.
Limit, direct, of magmas      I § no.
Limit, direct, of rings      I § no.
Limit, inverse, of $A_\alpha$ -algebras      III § no.
Limit, inverse, of $A_\alpha$ -modules      II § no.
Limit, inverse, of groups, of groups with operators, of monoids      I § no.
Limit, inverse, of magmas      I § no.
Limit, inverse, of rings      I § no.
Line (passing through 0) in a vector space      II § no.
Line, affine      II § nos.
Line, projective      II § no.
Linear equation, system      II § no.
Linear equation, system, homogeneous      II § no.
Linear form      II § no.
Linear group      II § no.
Linear group, special      III § no.
Linear mapping      II § no.
Linear mapping, function, affine      II § no.
Linear mapping, projective      II § no.
Linear problem      II § no.
Linear variety      II § nos. 7
Linear variety, affine      II § no.
Linear variety, projective      II § nos.
Linearity, principle of extension by      II § no.
Linearly dependent, linear independent, elements      II § no.
Linearly disjoint subalgebras      III § no.
M-morphism (M a monoid of operators)      I § no.
M-set (M a monoid of operators)      I § no.
Magma      I § no.
Magma of mappings into a magma      I § no.
Magma, associative      I § no.
Magma, commutative      I § no.
Magma, defined by generators and relations      I § no.
Magma, free, over a set      I § no.
Magma, opposite      I § no.
Magma, product      I § no.
Magma, quotient      I § no.
Magma, unital      I § no.
Magmas, isomorphic      I § no.
Mapping compatible with an action      I § no.
Mapping compatible with the operation of a monoid      I § no.
Mapping distributive with respect to a variable      I § no.
Mapping! linear, $A_s(T)\rightarrow E$ determined by a mapping $T \rightarrow E$       II § no.
Mapping, affine linear, affime      II § no.
Mapping, alternating multilinear      III § no.
Mapping, biadditive, $\bf{Z}$ -bilinear      II § no.
Mapping, C-bilinear      II § no.
Mapping, C-multilinear      II § no.
Mapping, linear, A-linear      II § no.
Mapping, linear, associated with an affine mapping      II § no.
Mapping, multiadditive, $\bf{Z}$ -multilinear      II § no.
Mapping, orbital      I § no.
Mapping, projective linear, projective      II § no.
Mapping, right invertible linear, left invertible linear      II § no.
Mapping, semi-linear      II § no.
Mapping, symmetric multilinear      III § no.
Matrices differing only by the order of the columns, rows      II § no.
Matrices, equivalent      II § no.
Matrices, similar square      II § no.
Matrix obtained by bordering a matrix      II § no.
Matrix obtained by suppressing columns, rows      II § no.
Matrix of a linear mapping with respect to two bases      II § no.
Matrix of a linear system      II § no.
Matrix of a permutation      II § no.
Matrix of a semi-linear mapping with respect to two bases      II § no.
Matrix of an element with respect to a basis      II § no.
Matrix of an endomorphism with respect to a basis      II § no.
Matrix of passing from one basis to another      II § no.
Matrix units      II § no.
Matrix with only zeros below (above) the diagonal      II § no.
Matrix, contragredient, of an invertible matrix      II § no.
Matrix, diagonal      II § no.
Matrix, empty      II § no.
Matrix, invertible      II § no.
Matrix, lower triangular, upper triangular      II § no.
Matrix, matrix of type (p, q)      II § no.
Matrix, monomial      II § no.
Matrix, scalar      II § no.
Matrix, square, square matrix of order n      II § no.
Matrix, unimodular      III § no.
Matrix, zero      II § no.
Maximal ideal      I § no.
Minimal normal stable subgroups      I § Exercise
Minimal simple group      I § Exercise
Minor, minor of order p of a matrix      III § no.
Minors, complementary      III § no.
Mixed tensor      III § no.
Module of finite length      II § no.
Module of formal linear combinations      II § no.
Module of linear relations      II § no.
Module over an algebra      III § no.
Module, bigraded      II § no.
Module, divisible      II § Exercise
Module, dual      II § no.
Module, faithful      II § no.
Module, faithful, associated with a module      II § no.
Module, free      II § no.
Module, graded free      II § no.
Module, graded quotient      II § no.
Module, graded, graded module with positive degrees      II § no.

Module, indecomposable      II § Exercise
Module, injective      II § Exercise
Module, left, right module, A-module      E § no.
Module, monogeneous      II § no.
Module, product      II § no.
Module, projective      II § no.
Module, quotient      II § no.
Module, reflexive      II § no.
Module, torsion, over an integral domain      II § no.
Module, torsion-free, over an integral domain      II § no.
Monogeneous group      I § no.
Monogenous module      II § no.
Monoid      I § no.
Monoid defined by generators and relations      I § no.
Monoid of differences      I § no.
Monoid of fractions with denominators in S      I § no.
Monoid operating faithfully on a set      I § no.
Monoid, free, over a set      I § no.
Monoidal sum      I § no.
Monomial      III § no.
Morphism of extensions      I § no.
Morphism, A-module      II § no.
Morphism, algebra      III § no.
Morphism, cogebra      III § no.
Morphism, graded bigebra, left graded bigebra morphism      III § no.
Morphism, graded cogebra      III § no.
Morphism, magma      I § no.
Morphism, monoid      I § no.
Morphism, ring      I § no.
Morphism, unital algebra      III § no.
Morphism, unital magma      I § no.
Multiadditive, $\bf{Z}$ -multilinear, mapping      II § no.
Multidegree in the free algebra of a monoid      III § Exercise
Multiindex      I § no.
Multilinear form      II § no.
Multimodule      II § no.
Multimodule, quotient      II § no.
Multiple, left, right      I § no.
Multiplication      I § no.
Multiplication in an algebra      III § no.
Multiplication table      III § no.
Multiplicative group of a ring      I § no.
M°-set opposite to an M-set      I § no.
n-form      III § no.
Negative of an element      I § no.
Negative rational integer      I § no.
Negative rational number      I § no.
Nielson-Schreier Theorem      I § Exercise
Nilpotent group, nilpotent group of class n      I § no.
Norm in a quadratic algebra      III § no.
Norm of a scalar relative to a module      III § no.
Norm of an element in a K-algebra relative to E      III § no.
Norm, Cayley      III § no.
Normal stable subgroup      I § no.
Normal subgroup      I § no.
normalizer      I § no.
Normalizing (element, subset) a subset      I § no.
Null element      I § no.
Number (rational), negative, positive, strictly negative, strictly positive      I § no.
Number, prime      I § no.
Number, rational      I § no.
Numerator      I § no.
Octonions of type ( $\alpha$ , $\beta$ , $\gamma$ , $\delta$ ) (algebra of)      III Appendix no.
Octonions, Cayley      III Appendix no.
Odd permutation      I § no.
Operation by left, right, translation      I § no.
Operation, left, right (laws of)      I § no.
Operation, left, right, of a monoid      I § no.
Operation, simply transitive      I § no.
Operation, transitive      I § no.
Operation, trivial      I § no.
Operator      I § no.
Opposite algebra      III § no.
Opposite cogebra      III § no.
Opposite law      I § no.
Opposite magma      I § no.
Opposite ring      I § no.
Opposite to an M-set, M°-set      I § no.
Orbit      I § no.
Orbital mapping      I § no.
Order of a cycle      I § no.
Order of a formal power series with respect to certain indeterminates      III § no.
Order of a group      I § no.
Order of a square matrix      II § no.
Order of an element in a group      I § no.
Order, element of infinite      I § no.
Order, total order, of a formal power series      III § no.
Ordered sequence      I § no.
Ordered sequences, similar      I § no.
Origin      I § no.
Origin, choice of, in an affine space      II § no.
Orthogonal elements, sets      II § no.
Orthogonal family of projectors      II § no.
Orthogonal, submodule, to a subset of E (resp. E*)      II § no.
p-group      I § no.
p-regular element      I § Exercise
p-unipotent element      I § Exercise
p-vector      III § no.
p-vector, pure      III § no.
Parallel linear varieties      II § no.
Parallelogram      II § Exercise
Parameters, direction, of an affine line      II § no.
Partial derivative      III § no.
Partial graduation      II § no.
Passage, matrix of      II § no.
Permutable elements      I § no.
Permutation, even, odd      I § no.
Plane passing through 0 in a vector space      II § no.
Plane, affine      II § nos.
Plane, projective      II § no.
Point of a projective space      II § no.
Point of an affine space      II § no.
Points at infinity      II § no.
Points, affinely independent      II § no 3
Polynomial containing no term in $X^\nu$       III § no.
Polynomial identities      III § no.
Polynomial of degree n      III § no.
Polynomial relators      III § no.
Polynomial with no constant term      III § no.
Polynomial with respect to a family of indeterminates, with coefficients in a ring      III § no.
Polynomial, characteristic, of a scalar with respect to a module      III §9 no.
Polynomial, characteristic, of an element in a K-algebra      III § no.
Polynomial, characteristic, of an endomorphism      III § no.
Positive rational integer      I § no.
Positive rational number      I § no.
Power, exterior, of a linear mapping      III § no.
Power, exterior, of a matrix      III § no.
Power, exterior, of a module      III § no.
Power, n-th, under an associative law      I § no.
Power, symmetric, of a linear mapping, of a module      III § no.
Power, tensorial, of a linear mapping      III § no.
Power, tensorial, of a module      III § no.
Presentation of a group      I § no.
Presentation of an algebra      III § no.
Presented, finitely (group)      I § Exercise
Preservation when passing to the quotient      I § no.
Prime ideal      I § no.
Prime number      I § no.
Prime, relatively (integers)      I § no.
Primitive element in a free group      I § Exercise
Primitive element in a free magma generated by a single element      I § Exercise
Primitive element of a graded bigebra      III §11 no.
Principal G-set, homogeneous      I § no.
Principal ideal      I § no.
Principal series      I § Exercise
Principal set under G, homogeneous      I § no.
Principle of extension by linearity      II § no.
Problem, linear      II § no.
Product algebra      III § no.
Product group with operators      I § no.

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