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

Natural projection      4.7 7.5 9.2 9.4 9.5 10.5
Natural transformation      10.3
Naturality      S3
Newton’s identities      A6
Nil ideal      9.7
Nilpotent element      8.6 9.7
Nilpotent group      5.7
Nilpotent ideal      9.7
Nilradical      8.6
Noetherian modules      4.6 7.5
Noetherian rings      4.6 7.5
Nonarchimedian absolute value      7.9
Noncommuting indeterminates      9.8
Nontrivial ideal      2.2
Norm      7.1 7.3
Normal closure      3.5
Normal extension      3.5
Normal series      5.6
Normal Sylow p-subgroup      5.5
normalizer      5.2
Nullstellensatz      8.3 8.4
Number field      7.1
Objects      10.1
Opposite category      10.1
Opposite ring      4.4
Orbit      5.2
Orbit-counting theorem      5.3
Orbit-stabilizer theorem      5.2
Order      1.1
Order ideal      4.2
Orthogonal idempotents      9.6
Ostrowski’s theorem      7.9
p-adic absolute value      7.9
p-adic integers      7.9
p-adic numbers      7.9
p-adic valuation      7.9
p-group      5.4
Perfect field      3.4
Permutation      1.2
Permutation group      1.2
Permutation module      9.5
Polynomial rings      2.1 2.5
Polynomials over a field      3.1
Power sums      A6
Preordered set      10.2
Primary component      A10
Primary decomposition      8.6
Primary ideal      8.6
Prime element      2.6
Prime ideal      2.4
Primitive element, theorem of      3.5 6.6
Primitive polynomial      2.9
Principal ideal domain      2.6
PRODUCT      10.2
Product of an ideal and a module      9.3
Product of ideals      2.3 8.5 7.6
Projection      4.7 9.2 9.4 9.5 10.5
Projection functor      10.3
Projective basis lemma      10.5
Projective limit      10.9
Projective modules      9.8 10.5
Projective resolution      S4
Proper ideal      2.2
Prufer group      A10
Pullback      10.6
Purely inseparable      3.4
Pushout      10.6
Quadratic extensions      6.3 7.2
Quasi-regular element      9.7
Quasicyclic group      A10
Quaternion group      2.1
Quaternions      2.1
Quotient field      2.8
Quotient group      1.3
Quotient ring      2.2
R-homomorphism on R      9.4
Rabinowitsch trick      8.4
Radical extension      6.8
Radical of an ideal      8.3
Rank of a free module      4.4
Rational integer      7.2
Rational root test      2.9
Rationals mod 1      1.1 (Problem 7) 10.4 10.6 A10
refinement      5.6
Regular action      5.1 5.2
Regular n-gon      6.8
Regular representation      9.5
Relatively prime ideals      2.3
Remainder theorem      2.5
Representation      9.5
Residue field      9.8
Resolvent cubic      A6
Restriction of scalars      8.7 10.8
Right adjoint      10.7
Right cancellable      10.1
Right derived functors      S5
Right exact functor      10.4

Right ideal      2.2
Right resolution      S4
Right-Noetherian ring      9.8
Right-quasiregular element      9.7
Right-semisimple ring      9.6
Ring      2.1
Ring of fractions      2.8 8.5
Schreier refinement theorem      5.6
Schur’s lemma      9.2
Semidirect product      5.8
Semigroup      1.1
Semisimple module      9.1
Semisimple ring      9.3
Separable element      3.4
Separable extension      3.4
Separable polynomial      3.4
Series for a module      7.5
Simple group      5.1 5.5
Simple left ideal      9.3
Simple module      7.5 9.1 9.2
Simple ring      9.3 9.5
Simplicity of the alternating group      5.6
Simultaneous basis theorem      4.6
Skew field      2.1
Smith normal form      4.5
Snake diagram      S2
Snake lemma      S2
Solvability by radicals      6.8
Solvable group      5.7
Spanning set      4.3 6.9
Special linear group      1.3
Split exact sequence      4.7 5.8
Splitting field      3.2
Squaring the circle      6.8
Standard representation of a p-adic integer      7.9
Steinitz exchange      6.9
Stickelberger’s theorem      7.4
Subcategory      10.3
Subgroup      1.1
Submodule      4.1
Subnormal series      5.6
Subring      2.1
Sum of ideals      2.2
Sum of modules      4.3
Sylow p-subgroup      5.4
Sylow theorems      5.4
Symmetric group      1.2 6.6
Symmetric polynomial      6.1
Tensor functors      10.3
Tensor product of matrices      8.7
Tensor product of module homomorphisms      8.7
Tensor product of modules      8.7
Terminal object      10.1
Tor      S5
Torsion Abelian group      8.7 (Problem 3) 10.2
Torsion element      4.6
Torsion module      4.6
Torsion subgroup      A10
Torsion submodule      4.6
Torsion-free module      4.6
Trace      7.3
Transcendence basis      6.9
Transcendence degree      6.9
Transcendental element      3.1
Transcendental extension      6.9
Transcendental number      3.3
Transitive action      5.2
Transitive subgroup of       6.3
Transitivity of algebraic extensions      3.3
Transitivity of separable extensions      3.4
Transitivity of trace and norm      7.3
Transposition      1.2
Trisecting the angle      6.8
Trivial absolute value      7.9
Trivial action      5.1 5.2
Twisted cubic      8.3
Two-sided ideal      2.2
Ultrametric inequality      7.9
Underlying functor      10.3
Unimodular matrix      7.4
Unique factorization domain      2.6
Unique factorization of ideals      7.7
UNIT      2.1
Universal mapping property (UMP)      8.7 10.2
Upper central series      5.7
Valuation      7.9
Valuation ideal      7.9
Valuation ring      7.9
Vandermonde determinant      A6 7.4
Vector space as an F [X]-module      4.1
Von Dyck’s theorem      5.8
Weak Nullstellensatz      8.3
Wedderburn structure theorem      9.5
Wedderburn — Artin theorem      9.4
Zariski topology      8.1
Zassenhaus lemma      5.6
Zero object      10.1

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