Differential Galois theory

• adele and idele
• differential galois theory

• Liouville 

 

elementary extension

• using exponential and logarithm
• elementary element

 

 

Liouville extension

• we can adjoin integrals and exponentials of integrals + algbraic extension
• an element is said to be representable by a generalized quadrature

 

Picard-Vessiot extension

• examples
  
  • algebraic extension
  • adjoining an integral
  • adjoining the exponential of an integral

 

theorem

If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable.

 

solution by quadrature

• QD. SOLUTION BY QUADRATURE

 

 

#

 

 

하위페이지

• 갈루아 이론
  
  • algebraic functions
    
  • Class Field Theory
    
  • Differential Galois theory
    
  • Liouville theory
    
  • number fields and threefolds
    
  • 대수적정수론
    

 

 

 

표준적인 도서 및 추천도서

• Abel_s_theorem_by_Arnold.djvu
  
• arnold book on abel theorem problem 348
  
• An introduction to differential algebra
  
  • Irving Kaplansky
    
• algebraic theory of differential equations
  

• http://gigapedia.info/1/galois_theory
• http://gigapedia.info/1/differential+galois+theory
• http://gigapedia.info/1/Kolchin
• http://gigapedia.info/1/ritt
• http://gigapedia.info/1/Galois'+dream
• http://gigapedia.info/1/differntial+algebra
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

• Algebraic Functions (Dover Phoenix Editions)
  
  • Gilbert Ames Bliss 
    
  • http://gigapedia.org/v5/item:view_links?id=100873
    

 

 

참고할만한 자료

• Determining the Galois Group of a Polynomial
• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Differential_Galois_theory
• http://en.wikipedia.org/wiki/Homotopy_lifting_property
• http://en.wikipedia.org/wiki/covering_space
• http://en.wikipedia.org/wiki/Field_extension