Picard–Vessiot theory

수학노트
둘러보기로 가기 검색하러 가기

노트

위키데이터

말뭉치

  1. However such an equation may have Picard-Vessiot extensions which are not formally real fields.[1]
  2. Picard–Vessiot theory was developed by Picard between 1883 and 1898 and by Vessiot from 1892–1904 (summarized in (Picard 1908, chapter XVII) and Vessiot (1892, 1910)).[2]
  3. We give a transparent proof that difference Picard-Vessiot theory is a part of the general difference Galois theory.[3]
  4. In this paper we obtain some consequences of the application of Picard-Vessiot differential Galois theory to Ziglin's theorem.[4]
  5. Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras.[5]
  6. In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions.[6]
  7. We give an application to the parameterized Picard-Vessiot theory...[7]
  8. We get, first, in Chapter 5, a development of Picard-Vessiot extensions.[8]
  9. Thus, this well-crafted book certainly serves its intended purpose well: it is a very good self-contained introduction to Picard-Vessiot theory.[8]
  10. So, Algebraic Groups and Differential Galois Theory succeeds in several ways: it serves the targeted graduate student as well as the more experienced mathematician new to Picard-Vessiot theory.[8]
  11. In this paper, we prove the existence of a real Picard-Vessiot extension for a homogeneous linear differential equation defined over a real differential field K with real closed field of constants.[9]
  12. –Vessiot ring plays an important role, since it is the Picard–Vessiot ring which is a torsor (principal homogeneous space) for the Galois group (scheme).[10]
  13. Like fields are simple rings having only (0) and (1) as ideals, the Picard–Vessiot ring is a differentially simple ring, i.e. a differential ring having only (0) and (1) as differential ideals.[10]

소스

  1. ↑ Picard-Vessiot Extensions of Real Differential Fields
  2. ↑ Picard–Vessiot theory
  3. ↑ Picard-Vessiot theory in general Galois theoryAll
  4. ↑ Picard-Vessiot Theory and Ziglin's Theorem
  5. ↑ A categorical approach to Picard-Vessiot theory
  6. ↑ An effective approach to Picard-Vessiot theory and the Jacobian Conjecture
  7. ↑ The Picard-Vessiot theory, constrained cohomology, and linear differential algebraic groups
  8. ↑ 8.0 8.1 8.2 Algebraic Groups and Differential Galois Theory
  9. ↑ [PDF Real Picard-Vessiot theory]
  10. ↑ 10.0 10.1 [PDF Picard–Vessiot theory of differentially simple rings]

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'picard'}, {'OP': '*'}, {'LOWER': 'vessiot'}, {'LEMMA': 'theory'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Picard–Vessiot_theory&oldid=51116"