Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 701-706
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N. V. Grigorenko. On Picard–Vessiot extensions of differential fields. Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 701-706. http://geodesic.mathdoc.fr/item/SM_1978_34_6_a0/
@article{SM_1978_34_6_a0,
author = {N. V. Grigorenko},
title = {On {Picard{\textendash}Vessiot} extensions of differential fields},
journal = {Sbornik. Mathematics},
pages = {701--706},
year = {1978},
volume = {34},
number = {6},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1978_34_6_a0/}
}
TY - JOUR
AU - N. V. Grigorenko
TI - On Picard–Vessiot extensions of differential fields
JO - Sbornik. Mathematics
PY - 1978
SP - 701
EP - 706
VL - 34
IS - 6
UR - http://geodesic.mathdoc.fr/item/SM_1978_34_6_a0/
LA - en
ID - SM_1978_34_6_a0
ER -
%0 Journal Article
%A N. V. Grigorenko
%T On Picard–Vessiot extensions of differential fields
%J Sbornik. Mathematics
%D 1978
%P 701-706
%V 34
%N 6
%U http://geodesic.mathdoc.fr/item/SM_1978_34_6_a0/
%G en
%F SM_1978_34_6_a0
A characterization is given of Picard–Vessiot elements over a partial differential field of characteristic zero. The structure of such elements that generate extensions of transcendence degree one is described. Bibliography: 6 titles.
[1] E. R. Kolchin, Differential algebra and algebraic groups, Academic Press, New York, 1973 | MR | Zbl
[2] E. R. Kolchin, “Constrained extentions of differential fields”, Advances in Math., 12 (1974), 141–170 | DOI | MR | Zbl
[3] E. R. Kolchin, “Some problems in differential algebra” (Moscow), Proc. Int. Congr. Math., 1966, 269–276, Moscow | MR
[4] E. R. Kolchin, “Galois theory of differential fields”, Amer. J. Math., 75, 1953 | MR | Zbl
[5] M. F. Singer, “Solutions of linear differential equations in functions fields of one variable”, Proc. Amer. Math. Soc., 54 (1976), 69–72 | DOI | MR | Zbl
