Picard–Vessiot theory

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위키데이터

• ID : Q7190519

말뭉치

1. However such an equation may have Picard-Vessiot extensions which are not formally real fields.
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)).
3. We give a transparent proof that difference Picard-Vessiot theory is a part of the general difference Galois theory.
4. In this paper we obtain some consequences of the application of Picard-Vessiot differential Galois theory to Ziglin's theorem.
5. Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras.
6. In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions.
7. We give an application to the parameterized Picard-Vessiot theory...
8. We get, first, in Chapter 5, a development of Picard-Vessiot extensions.
9. Thus, this well-crafted book certainly serves its intended purpose well: it is a very good self-contained introduction to Picard-Vessiot theory.
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.
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.
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).
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.

메타데이터

위키데이터

• ID : Q7190519