Generic rings for Picard–Vessiot extensions and generic differential equations
نویسندگان
چکیده
منابع مشابه
Generic Rings for Picard–Vessiot Extensions and Generic Differential Equations
Let G be an observable subgroup of GLn. We produce an extension of differential commutative rings generic for Picard–Vessiot extensions with
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The notion of a generic Picard-Vessiot extension with group G is equivalent to that of a generic linear differential equation for the same group.
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Let C be an algebraically closed field with trivial derivation and let F denote the differential rational field C〈Yij〉, with Yij , 1 ≤ i ≤ n − 1, 1 ≤ j ≤ n, i ≤ j, differentially independent over C. We show that there is a Picard-Vessiot extension E ⊃ F for a matrix equation X ′ = XA(Yij), with differential Galois group SOn, with the property that if F is any differential field with field of co...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2007
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2006.08.014