Algebraic D-groups and differential Galois theory
نویسندگان
چکیده
منابع مشابه
Algebraic D-groups and Differential Galois Theory
We discuss various relationships between the algebraic Dgroups of Buium, 1992, and differential Galois theory. In the first part we give another exposition of our general differential Galois theory, which is somewhat more explicit than Pillay, 1998, and where generalized logarithmic derivatives on algebraic groups play a central role. In the second part we prove some results with a “constrained...
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Quantifier Elimination We work in K a large rich differentially closed field. All other differential fields are assumed to be small subfields of K. Let L = {+,−, ·, δ, 0, 1} be the language of differential rings. We let L− = {+,−, ·, 0, 1}, the language of rings. If k is a differential field, we can view k either as an L-structure or an L−-structure. Theorem 1.1 (Quantifier Elimination) For any...
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The aim of the talk is to explain how to make these statements precise and prove them, using differential Galois theory. The reference to all of the material here is [vdPS03]. By solving a differential equation we mean obtaining a solution via a finite number of operations of the following kind (starting with a rational function): • Adding a function algebraic over the functions we already have...
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Differential Galois Theory is a branch of abstract algebra that studies fields equipped with a derivation function. In much the same way as ordinary Galois Theory studies field extensions generated by solutions of polynomials over a base field, differential Galois Theory studies differential field extensions generated by solutions to differential equations over a base field. In this paper, we w...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2004
ISSN: 0030-8730
DOI: 10.2140/pjm.2004.216.343