Algebra

Portada
Springer Science & Business Media, 6 dic 2012 - 914 páginas

"Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." NOTICES OF THE AMS

"The author has an impressive knack for presenting the important and interesting ideas of algebra in just the right way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." MATHEMATICAL REVIEWS

This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.

 

Páginas seleccionadas

Índice

Part One The Basic Objects of Algebra
2
Polynomials
6
Normal subgroups
13
Cyclic groups
23
Sylow subgroups
33
Finitely generated abelian groups
42
Inverse limit and completion
49
Free groups
66
Algebraic Spaces 377
378
Noetherian Rings and Modules
414
Real fields
451
Real zeros and homomorphisms
457
Absolute Values 465
466
Part Three Linear Algebra and Representations
501
Decomposition over one endomorphism
556
Structure of Bilinear Forms
572

Rings and homomorphisms
85
Commutative rings
92
Localization
107
Basic definitions
119
Direct products and sums of modules
127
Free modules
135
The dual space and dual module
142
EulerPoincaré maps
155
Part TWO Algebraic Equations
221
Transcendental Extensions 355
235
Galois Theory
262
Galois cohomology
302
Algebraic independence of homomorphisms
308
The modular connection
315
Extensions of Rings
335
The Tensor Product
602
Semisimplicity
642
Representations of Finite Groups
664
The Alternating Product
732
Part FOur Homological Algebra
759
Finite Free Resolutions
833
Finite free resolutions
839
Unimodular polynomial vectors
846
The Transcendence of e and T
867
Some Set Theory
875
Bibliography
895
194
901
571
903
601
909
Página de créditos

Términos y frases comunes

A-module abelian group additive algebraic apply associated assume automorphism basis called Chapter character characteristic closed coefficients commutative ring complex components conclude consider consisting contained Corollary cyclic define definition denote determined diagram dimension direct sum divides element equal Example Exercise exists expression extension fact factor field finite fixed follows function functor Furthermore given gives Hence homomorphism ideal immediately independent induced injective integer inverse irreducible isomorphism Lemma Let f Let G linear matrix maximal mean module morphism multiplicative normal object obtain obvious operation polynomial positive prime projective Proof Proposition prove reader relation representation representatives respect ring root satisfying separable Show simple subgroup submodule subset Suppose symmetric Theorem theory trivial unique unit variables vector space verified write zero

Información bibliográfica

TítuloAlgebra
Volumen 211 de Graduate Texts in Mathematics
AutorSerge Lang
Edición3, revisada
EditorSpringer Science & Business Media, 2012
ISBN146130041X, 9781461300410
N.º de páginas914 páginas
  
Exportar citaBiBTeX EndNote RefMan