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Beachy J.A. — Abstract Algebra II
Beachy J.A. — Abstract Algebra II



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Название: Abstract Algebra II

Автор: Beachy J.A.

Аннотация:

This volume offers a gentle introduction to proof in a concrete setting, the introduction of abstract concepts only after a careful study of important examples, and the gradual increase of the level of sophistication as one progresses through the book. It offers an extensive set of exercises that help to build proof writing skills. In addition, chapter introductions give motivation and historical context while tying the subject matter in with the broader picture.


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1996

Количество страниц: 144

Добавлена в каталог: 05.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action, linear      39
Adjoint, of a matrix      xiii
Algebra, division      100
Algebra, finite dimensional      99
Algebra, over a field      99
Algebraically closed field      137
Annihilates, of an element      14
Annihilator, of a module      56
Artin      100
Artinian module      67
Artinian ring      67
Ascending central series      31
Associated prime ideal      133
Automorphism, of a ring      15
Basis, for a module      52
Bicommutator, of a module      104
Bilinear function      83
Bimodule      89
Boolean ring      9
Center, of a ring      9
Central series, ascending      31
Chain      xiv
Closure, integral      126
Coefficient, leading      3
Cofactor, of a matrix      xiii
Completely prime ideal      12 100
Completely reducible module      64
Composition series, for a module      70
Cyclic module      51
Cyclic submodule      51
Dedekind      119
Dedekind domain      120
Degree, of a polynomial      3
Dense subring      114
Determinant      xii
Differential operators      4
Dimension, Krull      137
Direct product, of modules      60
Direct sum, of modules      60
Direct sum, of rings      6
Divisible module      83
Division algebra      100
Division ring      8
Divisor of zero      7
Domain      13
Domain, Dedekind      120
Domain, Euclidean      14
Domain, noncommutative      100
Element, idempotent      62
Element, integral      125
Element, invertible      7
Element, maximal      xiv
Element, nilpotent      15
Element, regular      7 13
Element, torsion      94
Essential submodule      106
Euclidean Domain      14
Extension, integral      125
Factor ring      12
Faithful module      56
Field      xi
Field of fractions      25
Field of quotients      25
Field, algebraically closed      137
Field, of rational functions      26
Finite length      72
Finitely generated module      51
Fitting's lemma      73
Fractional ideal      120
Frattini's argument      33
Free module      52
Frobenius      100
Function, bilinear      83
Generating set      51
Going down theorem      129
Going up theorem      128
Group ring      5 80
Group, nilpotent      31
Hamilton      9 99
hilbert      138
Hilbert basis theorem      68
Holomorph      36 38
Homogeneous component      106
Homomorphism, of rings      15
Homomorphism, split      63
Ideal      10
Ideal, completely prime      12 100
Ideal, fractional      120
Ideal, irreducible      132
Ideal, left      10 50
Ideal, maximal      12 13
Ideal, nil      110
Ideal, primary      132
Ideal, prime      12 101
Ideal, primitive      101
Ideal, principal      10
Ideal, right      10 50
Ideal, semiprime      101
Ideal, two-sided      10
Idempotent element      62
Idempotents, orthogonal      62
Incomparability theorem      128
Indecomposable module      73
Injective module      78
Integral closure      126
Integral domain      xi
Integral element      125
Integral extension ring      125
Integrally closed      126
Invertible element      7
Invertible fractional ideal      120
Irreducible ideal      132
Isomorphism      53
Isomorphism, of rings      15
Jacobson density theorem      114
Jacobson radical      106
Jordan — Holder      71
Kernel, of a ring homomorphism      16
Kernel, of an R-homomorphism      53
Kruii      137
Krull      137
Krull dimension      137
Lasker      119
Leading coefficient      3
Left ideal      10 50
Left ideal, maximal      55
Lemma, of Fitting      73
Lemma, of Nakayama      108
Lemma, of Schur      57
Lemma, of Zorn      xiv
Length, of a module      72
Linear action      39
Linear independence      52
Linear ordering      xiv
Localization of D at P      27
Localization of R at P      29
Lying over theorem      128
Macauley      119
Maschke's Theorem      80
Matrix unit      11
Maximal element      xiv
Maximal ideal      12 13
Maximal left ideal      55
Maximal submodule      55
Minimal submodule      57
Modular law      54
Module      49
Module, Artinian      67
Module, completely reducible      64
Module, cyclic      51
Module, divisible      83
Module, faithful      56
Module, finitely generated      51
Module, free      52
Module, indecomposable      73
Module, injective      78
Module, irreducible      57
Module, Noetherian      67
Module, nonsingular      117
Module, on the right      49
Module, prime      102
Module, projective      66
Module, semisimple      77
Module, simple      57
Module, singular      117
Module, torsion      69
Module, torsionfree      94
Multiplicative set      28
Nakayama's lemma      108
Nil ideal      110
Nil radical      131
Nilpotent element      15
Nilpotent group      31
Noether      119
Noetherian module      67
Noetherian ring      67
Nonsingular module      117
Nonsingular ring      117
Opposite ring      117
Ordering, linear      xiv
Ordering, partial      xiv
Orthogonal idempotents      62
Partial ordering      xiv
Polynomial ring      3
Power series, ring of      135
Primary ideal      132
Primary submodule      138
Prime ideal      12 101
Prime ideal, associated to Q      133
Prime module      102
Prime radical      131
Prime ring      12 101
Primitive ideal      101
Primitive ring      101
Principal ideal      10
Principal ideal domain      14
Principal ideal theorem      137
Principal ideal theorem, generalized      137
Principal left ideal      10
Product, semidirect      34 37
Projective module      66
Quaternions      8
R-automorphism      53
R-bilinear function      83
R-endomorphism      53
R-endomorphism ring      53
R-homomorphism      52
R-module      49
Radical      107
Radical, Jacobson      106
Radical, nil      131
Radical, of an ideal      132
Radical, prime      131
Rank, of a module      93
Rational function field      26
Regular element      7 13
Regular ring      115
Right ideal      10 50
Right R-module      49
Ring      ix
Ring automorphism      15
Ring homomorphism      15
Ring isomorphism      15
Ring, Artinian      67
Ring, boolean      9
Ring, commutative      x
Ring, group      5
Ring, group ring      80
Ring, Noetherian      67
Ring, nonsingular      117
Ring, of differential operators      4
Ring, of polynomials      3
Ring, of power series      135
Ring, opposite      117
Ring, prime      12 101
Ring, primitive      101
Ring, semiprime      101
Ring, semiprimitive      110
Ring, semisimple Artinian      113
Ring, simple      101
Ring, von Neumann regular      115
Schreier      71
Schur's lemma      57
Semidirect product      34 37
Semiprime ideal      101
Semiprime ring      101
Semiprimitive ring      110
Semisimple Artinian ring      113
Semisimple module      77
Set, multiplicative      28
Simple module      57
Simple ring      101
Singular module      117
Singular submodule      117
Small submodule      106
Socle      77
Split homomorphism      63
Submodule      50
Submodule, cyclic      51
Submodule, essential      106
Submodule, maximal      55
Submodule, minimal      57
Submodule, primary      138
Submodule, singular      117
Submodule, small      106
Submodule, superfluous      106
Subring      x 6
Subring, dense      114
Superfluous submodule      106
Tensor product      84
Theorem, generalized principal ideal      137
Theorem, going down      129
Theorem, going up      128
Theorem, incomparability      128
Theorem, Jacobson density      114
Theorem, lying over      128
Theorem, of Maschke      80
Theorem, principal ideal      137
Torsion element      94
Torsion module      69
Torsionfree module      94
Two-sided ideal      10
Unit element      7
Vector space      xv
von Neumann regular ring      115
Wedderburn      100
Well-ordered set      xiv
Zero divisor      7
Zorn's lemma      xiv
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