Field theory and polynomials Differential and difference algebra Concept
Picard–Vessiot extension
Summary
A Picard–Vessiot extension is the smallest differential field extension that contains a full set of solutions of a linear differential equation. It adds no new constants. It plays the role for linear differential equations that the splitting field plays for polynomial equations. Its group of differential automorphisms is the differential Galois group of the equation, the main object of differential Galois theory.
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| Tag | TB53Y5NMJD |
|---|---|
| URI | m2://TB53Y5NMJD |
| Kind | concept |
| Writing | W0 stub |
| MSC | 12H05, 34M15 |
| Specializes | Field extension |
| Changed | 2 November 2026 |
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