"Differential Galois theory"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
* adele and idele | * adele and idele | ||
* differential galois theory | * differential galois theory | ||
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* Liouville | * Liouville | ||
| 12번째 줄: | 9번째 줄: | ||
* using exponential and logarithm | * using exponential and logarithm | ||
| − | * | + | * elementary element |
| 20번째 줄: | 17번째 줄: | ||
<h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">Liouville extension</h5> | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">Liouville extension</h5> | ||
| − | * we can adjoin integrals and exponentials of integrals | + | * we can adjoin integrals and exponentials of integrals + algbraic extension |
| + | * an element is said to be representable by a generalized quadrature | ||
| 36번째 줄: | 34번째 줄: | ||
If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable. | If a Picard-Vessiot extension is a Liouville extension, then the Galois group of this extension is solvable. | ||
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| 61번째 줄: | 65번째 줄: | ||
* http://gigapedia.info/1/galois_theory | * http://gigapedia.info/1/galois_theory | ||
| − | * | + | |
| − | * | + | * http://gigapedia.info/1/differential+galois+theory |
| + | * http://gigapedia.info/1/Kolchin | ||
| + | * http://gigapedia.info/1/ritt | ||
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| + | * | ||
| + | ** <br> | ||
* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
* http://gigapedia.info/1/ | * http://gigapedia.info/1/ | ||
2009년 8월 27일 (목) 05:34 판
- adele and idele
- differential galois theory
- Liouville
elemetary 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.
하위페이지
표준적인 도서 및 추천도서
- Abel_s_theorem_by_Arnold.djvu
- arnold book on abel theorem problem 348
- http://gigapedia.info/1/differential+galois+theory
- http://gigapedia.info/1/Kolchin
- http://gigapedia.info/1/ritt
-
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- 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
- Gilbert Ames Bliss
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
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=