Ash R.B. — Abstract algebra: the basic graduate year :: Электронная библиотека попечительского совета мехмата МГУ

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Ash R.B. — Abstract algebra: the basic graduate year

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Название: Abstract algebra: the basic graduate year

Автор: Ash R.B.

Язык:

Рубрика: Математика/Алгебра/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 407

Добавлена в каталог: 12.03.2005

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Предметный указатель

Abelian category      10.4
Abelian group      1.1
Absolute value      7.9
Action of a group on a set      5.1
Adjoint Associativity      10.7
Adjoint functors      10.7
Affine n-space      8.1
Affine variety      8.1
AKLB setup      7.3
Algebra      4.1
Algebraic closure      3.3 10.9
Algebraic curve      8.3
Algebraic element      3.1
Algebraic extension      3.1
Algebraic function field      6.9
Algebraic geometry      8.1ff
Algebraic integers      7.1
Algebraic number      3.3 7.1
Algebraic number theory      7.1ff 7.3
Algebraically closed field      3.3
Algebraically independent set      6.9
Algebraically spanning set      6.9
Alternating group      1.2
Annihilator      4.2 9.2 9.7
Archimedian absolute value      7.9
Artin — Schreier theorem      6.7
Artinian modules      7.5
Artinian rings      7.5
Ascending chain condition (acc)      2.6 7.5
Associates      2.6
Associative law      1.1 2.1
Automorphism      1.3
Baer’s Criterion      10.6
Base change      10.8
Basis      4.3
Bilinear mapping      8.7
Binomial expansion modulo p      3.4
Binomial theorem      2.1
Boundary      S1
Canonical map      1.3
Category      10.1
Cauchy’s Theorem      5.4
Cayley’s Theorem      5.1
Center of a group      1.4
Center of a ring      4.1
Central series      5.7
centralizer      5.2
Chain complex      S1
Chain homotopy      S1
Chain map      S1
Chain rule      1.3 3.1
CHARACTER      6.1
Characteristic of a ring or field      2.1
Characteristic polynomial      7.3
Characteristic subgroup      5.7
Chief series      5.6
Chinese remainder theorem      2.3
Class equation      5.2
Cokernel      10.1
Colorings      5.3
Commutative diagram      1.4
Commutative ring      2.1
Commutator      5.7
Compatible morphisms      10.9
Complete ring of fractions      2.8
Composite of fields      3.1 6.2
Composition factors      5.6 7.5
Composition length      5.6 7.5
Composition of morphisms      10.1
Composition series      5.6 7.5
Conjugate elements      5.1 5.2
Conjugate subfields      6.2
Conjugate subgroups      5.1 6.2
Conjugates of a field ement      3.5
Conjugation      5.1 5.2-1
Connecting homomorphism      S2 S3
Constructible numbers and points      6.8
Content      2.9
Contravariant functor      10.3
Coproduct      10.2
Core      5.1
Correspondence theorem for groups      1.4
Correspondence theorem for modules      4.2
Correspondence theorem for rings      2.3
Coset      1.3
Counting two ways      5.3
Covariant functor      10.3
CYCLE      1.2 S1
Cyclic extension      6.7
Cyclic group      1.1
Cyclic module      4.2 9.1 9.2 9.7
Cyclotomic extension      5
Cyclotomic field      6.5 7.2
Cyclotomic polynomial      6.5
Decomposable module      9.6
Dedekind domain      7.6 7.7
Dedekind’s lemma      6.1 6.7 7.3 7.4
Degree      2.5
Deleted projective (or injective) resolution      S4
Derivative of a polynomial      3.4
Derived functors      S5
Derived length      5.7
Derived series      5.7
Descending chain condition      7.5
Diagram chasing      4.7
Differential      S1
Dihedral group      1.2 5.8 5.8
Dihedral group, (infinite dilhedral group)      9.5
Direct limit      10.9
Direct product of groups      1.5
Direct product of modules      4.3
Direct product of rings      2.3
Direct sum of modules      4.3
Direct system      10.9
Directed set      10.9
Discriminant      6.6 A6 7.4
Divides means contains      2.6 7.7
Divisible abelian group      A10
Divisible module      10.6
Division ring      2.1 9.1
Double centralizer      9.2
Double dual functor      10.3
Dual basis      7.4
Duality      10.1
Duplicating the cube      6.8
Eisenstein’s irreducibility criterion      2.9
Elementary divisors      4.6
Elementary symmetric functions      6.1
Embedding      3.3 3.5
Embedding in an injective module      10.7
Endomorphism      1.3 4.4
EPIC      10.1
Epimorphism      1.3
Equivalent absolute values      7.9
Equivalent matrices      4.4
Equivalent matrix representations      9.5
Euclidean Domain      2.7
Euler’s identity      2.1
Euler’s theorem      1.3
Evaluation map      2.1
Exact functor      8.5 10.4
Exact sequence      4.7
Exponent of a group      1.1 6.4
Ext      S5
Extension of a field      3.1
Extension of scalars      8.7 10.8
Exterior algebra      8.8
F-isomorphism, etc.      3.2
Factor theorem for groups      1.4
Factor theorem for modules      4.2

Factor theorem for rings      2.3
Faithful action      5.1
Faithful module      7.1 9.2 9.4
Faithful representation      9.5
Fermat primes      6.8
Fermat’s Little Theorem      1.3
Field      2.1
Field discriminant      7.4
Finite abelian groups      4.6
Finite extension      3.1
Finite fields      6.4
Finitely cogenerated module      7.5
Finitely generated algebra      10.8
Finitely generated module      4.4
Finitely generated submodule      7.5
Five lemma      4.7
Fixed field      6.1
Fixing group      6.1
Flat modules      10.8
Forgetful functor      10.3
Formal power series      2.1 8.2
Four group      1.2 1.5 A6
Four lemma      4.7
Fractional ideal      7.6
Frattini argument      5.8-2
Free abelian gup functor      10.3
Free group      5.8-1
Free module      4.3
Free product      10.2-2
Frobenius automorphism      3.4 6.4
Full functor      10.3
Full ring of fractions      2.8
Full subcategory      10.3
functor      10.3
Fundamental decomposition theorem (for finitely generated modules over a PID)      4.6
Fundamental Theorem of Galois Theory      6.2-1
Galois extension      3.5 6.1ff
Galois group      3.5 6.1ff
Galois group of a cubic      6.6
Galois group of a polynomial      6.3
Galois group of a quadratic      6.3
Galois group of a quartic      A6
Gaussian integers      2.1 2.7
Gauss’ Lemma      2.9
General equation of degree n      6.8
General linear group      1.3
Generating set      4.3
Generators and relations      1.2 4.6 5.8
Greatest common divisor      2.6 7.7
Group      1.1
Group algebra      9.5
Group representations      9.5
Group ring      9.5
Hermite normal form      4.5
Hilbert basis theorem      8.2
Hilbert’s Nullstellensatz      8.3 8.4
Hilbert’s Theorem      90 7.3
Hom functors      10.3-1
Homology functors      S1
Homology group      S1
Homology module      S1
Homomorphism from R to M determined by what it does to the identity      9.4 S6
Homomorphism of algebras      4.1
Homomorphism of groups      1.3
Homomorphism of modules      4.1
Homomorphism of rings      2.2
Hopkins — Levitzki theorem      9.8
Hypersurface      8.2
Ideal      2.2 8.1
Ideal class group      7.8
Idempotent linear transformation      9.5
Image      2.3 4.1
Indecomposable module      9.6
INDEX      1.3
Inductive limit      10.9
Initial object      10.1
Injection (inclusion)      4.7
Injective hull      10.7
Injective modules      10.6
Injective resolution      S4
Inner automorphism      1.4 5.7
Integral basis      7.2 7.4
Integral closure      7.1
Integral domain      2.1
Integral extensions      7.1
Integral ideal      7.6
Integrally closed      7.1
Invariant factors      4.5
Inverse limit      10.9
Inverse system      10.9
Inversions      1.2
Irreducible element      2.6
Irreducible ideal      8.6
Irreducible polynomial      2.9
Irreducible variety      8.1
Isomorphic groups      1.1
Isomorphism      1.3
Isomorphism extension theorem      3.2
Isomorphism Theorems for groups      1.4
Isomorphism Theorems for modules      4.2
Isomorphism Theorems for rings      2.3
Jacobson radical      9.7
Jacobson’s theorem      9.2
Jordan — Holder theorem      5.6 7.5
Kernel      1.3 2.2 10.1
Kernel of an action      5.1
Kronecker product of matrices      8.7
Krull — Schmidt theorem      9.6
Kummer extension      6.7
Lagrange interpolation formula      2.5
Lagrange’s Theorem      1.3
Laurent series      7.9
Leading coefficient      2.5
Least common multiple      2.6 7.7
Left adjoint      10.7
Left cancellable      10.1
Left derived functors      S5
Left exact functor      10.4
Left ideal      2.2
Left resolution      S4
Left-Noetherian ring      9.8
Left-quasiregular element      9.7
Left-semisimple ring      9.6
Length of a module      7.5
Lifting of a map      4.3 10.2
Linearly indepdent set      4.3
Local ring      2.4 7.9 8.5
localization      2.8 8.5
Long division      6.4
Long exact homology sequence      S3
Maschke’s Theorem      9.6
Matrices      2.1 4.4
Maximal ideal      2.4 8.3
Maximal submodule      9.7
Metric      7.9
Minimal generating set      9.8
Minimal left ideal      9.3
Minimal polynomial      3.1
Minimal prime ideal      8.4
Modding out      5.7
Modular law      4.1
Module      4.1
Modules over a principal ideal domain      4.6 10.5
Monic      10.1
Monoid      1.1
Monomorphism      1.3
Morphism      10.1
Nakayama’s Lemma      9.8
Natural action      5.3 6.3
Natural map      1.3

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