We present a simple proof of the theorem which says that for a series of extensions of differential fields K ⊂ L ⊂ M, where K ⊂ M is Picard-Vessiot, the extension K ⊂ L is Picard-Vessiot iff the differential Galois group is a normal subgroup of . We also present a proof that the probability function Erf(x) is not an elementary function.
@article{bwmeta1.element.bwnjournal-article-cmv84i1p173bwm,
author = {Henryk \.Zo\l \k adek},
title = {Two remarks about Picard-Vessiot extensions and elementary functions},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {173-183},
zbl = {1003.12002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p173bwm}
}
Żołądek, Henryk. Two remarks about Picard-Vessiot extensions and elementary functions. Colloquium Mathematicae, Tome 84/85 (2000) pp. 173-183. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p173bwm/
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