Difference between revisions of "Galois differential group"
From Encyclopedia of Mathematics
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| − | The group of all automorphisms of a [[Differential field|differential field]] | + | {{TEX|done}} |
| + | The group of all automorphisms of a [[Differential field|differential field]] $P$ that commute with derivations (cf. [[Derivation in a ring|Derivation in a ring]]) and that leave all elements of some fixed differential subfield of $P$ invariant. | ||
Latest revision as of 13:06, 9 August 2014
The group of all automorphisms of a differential field $P$ that commute with derivations (cf. Derivation in a ring) and that leave all elements of some fixed differential subfield of $P$ invariant.
Comments
Just as Galois theory has things to say about (solving) algebraic equations, so differential Galois theory (or the Galois theory of differential fields) is relevant to (solving) algebraic differential equations. For an account of differential Galois theory see Extension of a differential field and the references given there.
How to Cite This Entry:
Galois differential group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Galois_differential_group&oldid=15153
Galois differential group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Galois_differential_group&oldid=15153
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article