Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Jacobson N. — The Theory of Rings
Jacobson N. — The Theory of Rings

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: The Theory of Rings

Автор: Jacobson N.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1943

Количество страниц: 150

Добавлена в каталог: 21.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\Omega$-groups      5
$\Phi$-ring      55
Algebra over a field      55
Algebra over a field, defined by a group      56
Algebra over a field, isomorphism with a matrix algebra      56
Anti-homomorphism of a ring      16
Brauer group of algebras      105
Center of a ring      22 (footnote)
centralizer      103
Chain conditions      7
Chain conditions, rings satisfying descending condition      70
Completely primary ring      57
Completely reducible group      13
Completely reducible group, ring of endomorphisms of      58
Composites of fields      97
Composition series      7
Crossed products      82
Crossed products, direct products of      109
Decomposition of an arbitrary algebra      116
Derivation      101
Direct product of algebras      88
Direct product of crossed products      109
Direct product of fields      96
Direct sums of groups      10
Direct sums of ideals      62
Discriminant of an algebra      113
Division algebras, decomposition into division algebras of prime power degrees      110
Division algebras, degree of      104
Division algebras, over special fields      110
Elementary divisors      44
Elementary matrices      21
Endomorphism of a group      2
Endomorphism of a group, normal      8
Extension of isomorphism between simple subalgebras of a central simple algebra      101
Extension of isomorphism between subfields of a division ring      46
Extension of the field of an algebra      89
Factor set      80
First isomorphism theorem      6
Fitting’s Lemma      9
g-integral      122
Galois theory of division rings      84—86
Groupoid      132
Groupoid of normal ideals      134
Ideals, bounded      38 120
Ideals, capacity of maximal      45 123
Ideals, conjunctive      134
Ideals, distance      134
Ideals, fractional      119
Ideals, integral      120
Ideals, inverse of      120
Ideals, normal      131
Integral closure      122
Invariant factors      49
Involutorial anti-automorphism      24
Jordan — Holder — Schreier theorem      6
Krull — Schmidt theorem      11
Krull — Schmidt theorem, dual of      35
Linear transformation      21
Matrix rings      19 (footnote)
Matrix rings, isomorphism of      25
Minimum polynomial of a matrix (Theorem of Frobenius)      52
Minimum polynomial of an algebra      112
Minimum polynomial of an element of an algebra      110
Modules      14
Modules, bounded      47 129
Modules, conjunctive      137
Modules, cyclic      33
Modules, finitely generated      31 43
Modules, free      32
Modules, left      16
Modules, order of an element in      33
Nil ring      63
Nilpotent ring      63
Non-commutative polynomial domains      29 35 38 40 46
Norm theorems for division rings      47
Orders      119
Orders, bounded      120
Orders, bounded in an algebra      123
Orders, bounded of an ideal      120
Orders, bounded, equivalent      119
Orders, bounded, factorization of normal ideals in      136
Orders, bounded, factorization of two-sided ideals in      126
Orders, bounded, maximal      121
Primary ring      71
Principal ideal domains      30
Principal ideal domains, embedding in division rings      31
Principal ideal domains, factorization of elements in      34
Principal ideal domains, factorization of two-sided ideals in      37
Principal ideal domains, indecomposable elements in      35
Principal ideal domains, matrices with elements in      41
Principal ideal domains, similarity of elements in      33
Principal ideal rings      75—77
Principal ideal rings, modules relative to      77—79
Principal polynomial, trace and norm      113
Projective representations of a group      80
Quotient ring      118
Radical of a ring of endomorphisms      60
Radical of an abstract ring      64
Real quaternions      111
Real quaternions, algebraic closure of      36
Real quaternions, similarity of matrices over      51
Representation of a ring      14
Representation of a ring, left regular      16
Representation of a ring, regular      15 71—75
Representation of an algebra by matrices      91
Representation of an algebra by matrices with elements in another algebra      94
Representation of an algebra by matrices, complete reducibility for semi-simple algebras      94
Representation space      91
Ring of linear transformations      21
Ring of linear transformations, automorphisms and anti-automorphisms of      23
Ring of linear transformations, commuting subrings of      24
Ring of linear transformations, decomposition into irreducible right ideals      23
Ring of linear transformations, simplicity of      23
Schur’s lemma      57
Second isomorphism theorem      6
Semi-linear transformations      26 49—53
Semi-linear transformations, finite groups of      86
Semi-simple ring      64
Semi-simple ring, representation of      68—70
Semi-simple ring, structure of      64—68
Separability of an algebra      115
Separability of an algebra, discriminant criterion for      116
Similarity of elements      33
Similarity of ideals      130 137 138
Similarity of matrices      50
Simple algebra, central      98
Simple algebra, commuting subalgebras of      103
Simple algebra, exponent of      109
Simple algebra, index of      104
Simple algebra, separable subfields of      106
Simple algebra, simple subalgebras of      101
Simple algebra, structure of (Wedderburn’s Theorem)      98
Simple algebra, subfields of      104
Simple ring      23
Simple ring, structure of      67
Splitting fields      104
Total divisor      40
Vector space      17
Vector space, dimensionality of      18
Vector space, over different division rings      21
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте