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The Picard–Vessiot Antiderivative Closure
- Source :
- Journal of Algebra. 244(1):1-18
- Publication Year :
- 2001
- Publisher :
- Elsevier BV, 2001.
-
Abstract
- F is a differential field of characteristic zero with algebraically closed field of constants C . A Picard–Vessiot antiderivative closure of F is a differential field extension E ⊃ F which is a union of Picard–Vessiot extensions of F , each obtained by iterated adjunction of antiderivatives, and such that every such Picard–Vessiot extension of F has an isomorphic copy in E . The group G of differential automorphisms of E over F is shown to be prounipotent. When C is the complex numbers and F = C ( t ) the rational functions in one variable, G is shown to be free prounipotent.
Details
- ISSN :
- 00218693
- Volume :
- 244
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra
- Accession number :
- edsair.doi.dedup.....e38dad6ad917aabd3140b34826bbb7d2
- Full Text :
- https://doi.org/10.1006/jabr.2001.8876