李代数和代数群 本书特色

陶威尔编著的《李代数和代数群》内容介绍： the theory of groups and lie algebras is interesting for many reasons. in the mathematical viewpoint, it employs at the same time algebra, analysis and geometry. on the other hand, it intervenes in other areas of science, in particular in different branches of physics and chemistry. it is an active domain of current research. one of the difficulties that graduate students or mathematicians interested in the theory come across, is the fact that the theory has very much advanced,and consequently, they need to read a vast amount of books and articles before they could tackle interesting problems.

李代数和代数群 目录

1　results on topological spaces
　1.1　irreducible sets and spaces
　1.2　dimension
　1.3　noetherian spaces
　1.4　constructible sets
　1.5　gluing topological spaces
2　rings and modules
　2.1　ideals
　2.2　prime and maximal ideals
　2.3　rings of fractions and localization
　2.4　localizations of modules
　2.5　radical of an ideal
　2.6　local rings
　2.7　noetherian rings and modules
　2.8　derivations
　2.9　module of differentials
3　integral extensions
　3.1　integral dependence
　3.2　integrally closed domains
　3.3　extensions of prime ideals
4　factorial rings
　4.1　generalities
　4.2　unique factorization
　4.3　principal ideal domains and euclidean domains
　4.4　polynomials and factorial rings
　4.5　symmetric polynomials
　4.6　resultant and discriminant
　field extensions
　5.1　extensions
　5.2　algebraic and transcendental elements
　5.3　algebraic extensions
　5.4　transcendence basis
　5.5　norm and trace
　5.6　theorem of the primitive element
　5.7　going down theorem
　5.8　fields and derivations
　5.9　conductor
　finitely generated algebras
　6.1　dimension
　6.2　noether's normalization theorem
　6.3　krull's principal ideal theorem
　6.4　maximal ideals
　6.5　zariski topology
7　 gradings and filtrations
　7.1　graded rings and graded modules
　7.2　graded submodules
　7.3　applications
　7.4　filtrations
　7.5　grading associated to a filtration
　inductive limits
　8.1　generalities
　8.2　inductive systems of maps
　8.3　inductive systems of magmas, groups and rings
　8.4　an example
　8.5　inductive systems of algebras
　sheaves of functions
　9.1　sheaves
　9.2　morphisms
　9.3　sheaf associated to a presheaf
　9.4　gluing
　 9.5　ringed space
10 jordan decomposition and some basic results on groups
　 10.1 jordan decomposition
　 10.2 generalities on groups
　 10.3 commutators
　 10.4 solvable groups
　 10.5 nilpotent groups
　10.6 group actions
　10.7 generalities on representations
　10.8 examples
11 algebraic sets
　11.1 affine algebraic sets
　11.2 zariski topology
　11.3 regular functions
　11.4 morphisms
　11.5 examples of morphisms
　11.6 abstract algebraic sets
　11.7 principal open subsets
　11.8 products of algebraic sets
12 prevarieties and varieties
　12.1 structure sheaf
　12.2 algebraic prevarieties
　12.3 morphisms of prevarieties
　12.4 products of prevarieties
　12.5 algebraic varieties
　12.6 gluing
　12.7 rational functions
　12.8 local rings of a variety
13 projective varieties
　13.1 projective spaces
　13.2 projective spaces and varieties
　13.3 cones and projective varieties
　13.4 complete varieties
　13.5 products
　13.6 grassmannian variety
14 dimension
　14.1 dimension of varieties
　14.2 dimension and the number of equations .
　14.3 system of parameters
　14.4 counterexamples
15 morphisms and dimenion
　15.1 criterion of affineness
　15.2 afiine morphisms
　15.3 finite morphisms
　15.4 factorization and applications
　15.5 dimension of fibres of a morphism
　15.6 an example
16 tangent spaces

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自然科学 数学 代数数论组合理论

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