Algebra / Serge Lang.

Por: Lang, Serge, 1927-2005Series Addison-Wesley series in mathematicsEditor: Reading, Mass. : Addison-Wesley, c1965Descripción: xvii, 508 p. ; 24 cmTema(s): AlgebraOtra clasificación: 00A05
Contenidos:
Part One
Groups, Rings, and Modules
Chapter I
 Groups
1. Monoids [5]
2. Groups [9]
3. Cyclic groups [13]
4. Normal subgroups [14]
5. Operation of a group on a set [19]
6. Sylow subgroups [23]
7. Categories and functors [25]
8. Free groups [33]
9. Direct sums and free abelian groups [40]
10. Finitely generated abelian groups [45]
11. The dual group [50]
Chapter II
 Rings
1. Rings and homomorphisms [56]
2. Commutative rings [62]
3. Localization [66]
4. Principal rings [70]
Chapter III
 Modules
1. Basic definitions [74]
2. The group of homomorphisms [76]
3. Direct products and sums of modules [79]
4. Free modules [84]
5. Vector spaces [85]
6. The dual space [88]
Chapter IV
 Homology
1. Complexes [94]
2. Homology sequence [95]
3. Euler characteristic [98]
4. The Jordan-Hdlder theorem [192]
Chapter V
 Polynomials
1. Free algebras [106]
2. Definition of polynomials [110]
3. Elementary properties of polynomials [115]
4. The Euclidean algorithm [120]
5. Partial fractions [123]
6. Unique factorization in several variables [126]
7. Criteria for irreducibility [128]
8. The derivative and multiple roots [130]
9. Symmetric polynomials [132]
10. The resultant [135]
Chapter VI
Noetherian Rings and Modules
1. Basic criteria [142]
2. Hilbert’s theorem [144]
3. Power series [146]
4. Associated primes [148]
5. Primary decomposition [152]
Part Two
Field Theory
Chapter VII
Algebraic Extensions
1. Finite and algebraic extensions [161]
2. Algebraic closure [166]
3. Splitting fields and normal extensions [173]
4. Separable extensions [176]
5. Finite fields [182]
6. Primitive elements [185]
7. Purely inseparable extensions [186]
Chapter VIII
Galois Theory
1. Galois extensions [192]
2. Examples and applications [199]
3. Roots of unity [203]
4. Linear independence of characters [208]
5. The norm and trace [210]
6. Cyclic extensions [213]
7. Solvable and radical extensions [216]
8. Kummer theory [218]
9. The equation Xn — a = 0 [221]
10. Galois cohomology [224]
11. Algebraic independence of homomorphisms [225]
12. The normal basis theorem [229]
Chapter IX
Extensions of Rings
1. Integral ring extensions [237]
2. Integral Galois extensions [244]
3. Extension of homomorphisms [249]
Chapter X
Transcendental Extensions
1. Transcendence bases [253]
2. Hilbert’s Nulls tellensatz [255]
3. Algebraic sets [257]
4. Noether normalization theorem [260]
5. Linearly disjoint extensions [261]
6. Separable extensions [264]
7. Derivations [266]
Chapter XI
Real Fields
1. Ordered fields [271]
2. Real fields [273]
3. Real zeros and homomorphisms [278]
Chapter XII
Absolute Values
1. Definition, dependence, and independence [283]
2. Completions [286]
3. Finite extensions [292]
4. Valuations [296]
5. Completions and valuations [304]
6. Discrete valuations [305]
7. Zeros of polynomials over complete fields [308]
Part Three
Linear Algebra and Representations
Chapter XIII
Matrices and Linear Maps
1. Matrices [321]
2. The rank of a matrix [323]
3. Matrices and linear maps [324]
4. Determinants [328]
5. Duality [337]
6. Matrices and bilinear forms [342]
7. Sesquilinear duality [346]
Chapter XIV
Structure of Bilinear Forms
1. Preliminaries, orthogonal sums [354]
2. Quadratic maps [357]
3. Symmetric forms, orthogonal bases [358]
4. Hyperbolic spaces [359]
5. Witt’s theorem [360]
6. The Witt group [363]
7. Symmetric forms over ordered fields [365]
8. The Clifford algebra [367]
9. Alternating forms [370]
10. The Pfaffian [372]
11. Hermitian forms [374]
12. The spectral theorem (hermitian case) [376]
13. The spectral theorem (symmetric case) [378]
Chapter XV
Representation of One Endomorphism
1. Representations [384]
2. Modules over principal rings [386]
3. Decomposition over one endomorphism [395]
4. The characteristic polynomial [399]
Chapter XVI
Multilinear Products
1. Tensor product [408]
2. Basic properties [412]
3. Extension of the base [418]
4. Tensor product of algebras [420]
5. The tensor algebra of a module [421]
6. Alternating products [424]
7. Symmetric products [427]
8. The Euler-Grothendieck ring [429]
9. Some functorial isomorphisms [431]
Chapter XVII
 Semisimplicity
1. Matrices and linear maps over non-commutative rings [438]
2. Conditions defining semisimplicity [441]
3. The density theorem [443]
4. Semisimple rings [446]
5. Simple rings [448]
Chapter XVIII
Representations of Finite Groups
1. Semisimplicity of the group algebra [453]
2. Characters [455]
3. One-dimensional representations [459]
4. The space of class functions [461]
5. Orthogonality relations [465]
6. Induced characters [468]
7. Induced representations [471]
8. Positive decomposition of the regular character [475]
9. Supersolvable groups [478]
10. Brauer’s theorem [480]
11. Field of definition of a representation [485]
Appendix. The transcendence of e and п [493]
Index [501]
    Average rating: 0.0 (0 votes)
Item type Home library Shelving location Call number Materials specified Status Date due Barcode Course reserves
Libros Libros Instituto de Matemática, CONICET-UNS
Libros ordenados por tema 00A05A L269 (Browse shelf) Available A-2364

COMPLEMENTOS DE ÁLGEBRA

ESTRUCTURAS ALGEBRAICAS I


Bibliografía: p. xii.

Part One --
Groups, Rings, and Modules --
Chapter I --
Groups --
1. Monoids [5] --
2. Groups [9] --
3. Cyclic groups [13] --
4. Normal subgroups [14] --
5. Operation of a group on a set [19] --
6. Sylow subgroups [23] --
7. Categories and functors [25] --
8. Free groups [33] --
9. Direct sums and free abelian groups [40] --
10. Finitely generated abelian groups [45] --
11. The dual group [50] --
Chapter II --
Rings --
1. Rings and homomorphisms [56] --
2. Commutative rings [62] --
3. Localization [66] --
4. Principal rings [70] --
Chapter III --
Modules --
1. Basic definitions [74] --
2. The group of homomorphisms [76] --
3. Direct products and sums of modules [79] --
4. Free modules [84] --
5. Vector spaces [85] --
6. The dual space [88] --
Chapter IV --
Homology --
1. Complexes [94] --
2. Homology sequence [95] --
3. Euler characteristic [98] --
4. The Jordan-Hdlder theorem [192] --
Chapter V --
Polynomials --
1. Free algebras [106] --
2. Definition of polynomials [110] --
3. Elementary properties of polynomials [115] --
4. The Euclidean algorithm [120] --
5. Partial fractions [123] --
6. Unique factorization in several variables [126] --
7. Criteria for irreducibility [128] --
8. The derivative and multiple roots [130] --
9. Symmetric polynomials [132] --
10. The resultant [135] --
Chapter VI --
Noetherian Rings and Modules --
1. Basic criteria [142] --
2. Hilbert’s theorem [144] --
3. Power series [146] --
4. Associated primes [148] --
5. Primary decomposition [152] --
Part Two --
Field Theory --
Chapter VII --
Algebraic Extensions --
1. Finite and algebraic extensions [161] --
2. Algebraic closure [166] --
3. Splitting fields and normal extensions [173] --
4. Separable extensions [176] --
5. Finite fields [182] --
6. Primitive elements [185] --
7. Purely inseparable extensions [186] --
Chapter VIII --
Galois Theory --
1. Galois extensions [192] --
2. Examples and applications [199] --
3. Roots of unity [203] --
4. Linear independence of characters [208] --
5. The norm and trace [210] --
6. Cyclic extensions [213] --
7. Solvable and radical extensions [216] --
8. Kummer theory [218] --
9. The equation Xn — a = 0 [221] --
10. Galois cohomology [224] --
11. Algebraic independence of homomorphisms [225] --
12. The normal basis theorem [229] --
Chapter IX --
Extensions of Rings --
1. Integral ring extensions [237] --
2. Integral Galois extensions [244] --
3. Extension of homomorphisms [249] --
Chapter X --
Transcendental Extensions --
1. Transcendence bases [253] --
2. Hilbert’s Nulls tellensatz [255] --
3. Algebraic sets [257] --
4. Noether normalization theorem [260] --
5. Linearly disjoint extensions [261] --
6. Separable extensions [264] --
7. Derivations [266] --
Chapter XI --
Real Fields --
1. Ordered fields [271] --
2. Real fields [273] --
3. Real zeros and homomorphisms [278] --
Chapter XII --
Absolute Values --
1. Definition, dependence, and independence [283] --
2. Completions [286] --
3. Finite extensions [292] --
4. Valuations [296] --
5. Completions and valuations [304] --
6. Discrete valuations [305] --
7. Zeros of polynomials over complete fields [308] --
Part Three --
Linear Algebra and Representations --
Chapter XIII --
Matrices and Linear Maps --
1. Matrices [321] --
2. The rank of a matrix [323] --
3. Matrices and linear maps [324] --
4. Determinants [328] --
5. Duality [337] --
6. Matrices and bilinear forms [342] --
7. Sesquilinear duality [346] --
Chapter XIV --
Structure of Bilinear Forms --
1. Preliminaries, orthogonal sums [354] --
2. Quadratic maps [357] --
3. Symmetric forms, orthogonal bases [358] --
4. Hyperbolic spaces [359] --
5. Witt’s theorem [360] --
6. The Witt group [363] --
7. Symmetric forms over ordered fields [365] --
8. The Clifford algebra [367] --
9. Alternating forms [370] --
10. The Pfaffian [372] --
11. Hermitian forms [374] --
12. The spectral theorem (hermitian case) [376] --
13. The spectral theorem (symmetric case) [378] --
Chapter XV --
Representation of One Endomorphism --
1. Representations [384] --
2. Modules over principal rings [386] --
3. Decomposition over one endomorphism [395] --
4. The characteristic polynomial [399] --
Chapter XVI --
Multilinear Products --
1. Tensor product [408] --
2. Basic properties [412] --
3. Extension of the base [418] --
4. Tensor product of algebras [420] --
5. The tensor algebra of a module [421] --
6. Alternating products [424] --
7. Symmetric products [427] --
8. The Euler-Grothendieck ring [429] --
9. Some functorial isomorphisms [431] --
Chapter XVII --
Semisimplicity --
1. Matrices and linear maps over non-commutative rings [438] --
2. Conditions defining semisimplicity [441] --
3. The density theorem [443] --
4. Semisimple rings [446] --
5. Simple rings [448] --
Chapter XVIII --
Representations of Finite Groups --
1. Semisimplicity of the group algebra [453] --
2. Characters [455] --
3. One-dimensional representations [459] --
4. The space of class functions [461] --
5. Orthogonality relations [465] --
6. Induced characters [468] --
7. Induced representations [471] --
8. Positive decomposition of the regular character [475] --
9. Supersolvable groups [478] --
10. Brauer’s theorem [480] --
11. Field of definition of a representation [485] --
Appendix. The transcendence of e and п [493] --
Index [501] --

MR, 33 #5416

There are no comments on this title.

to post a comment.

Click on an image to view it in the image viewer

¿Necesita ayuda?

Si necesita ayuda para encontrar información, puede visitar personalmente la biblioteca en Av. Alem 1253 Bahía Blanca, llamarnos por teléfono al 291 459 5116, o enviarnos un mensaje a biblioteca.antonio.monteiro@gmail.com

Powered by Koha