Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 2, pp. 585-594
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A. Yu. Pirkovskii. On the conditions ensuring the freedom of topological modules over algebras of holomorphic functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 2, pp. 585-594. http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a8/
@article{FPM_1998_4_2_a8,
author = {A. Yu. Pirkovskii},
title = {On the~conditions ensuring the~freedom of topological modules over algebras of holomorphic functions},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {585--594},
year = {1998},
volume = {4},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a8/}
}
TY - JOUR
AU - A. Yu. Pirkovskii
TI - On the conditions ensuring the freedom of topological modules over algebras of holomorphic functions
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 1998
SP - 585
EP - 594
VL - 4
IS - 2
UR - http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a8/
LA - ru
ID - FPM_1998_4_2_a8
ER -
%0 Journal Article
%A A. Yu. Pirkovskii
%T On the conditions ensuring the freedom of topological modules over algebras of holomorphic functions
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1998
%P 585-594
%V 4
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a8/
%G ru
%F FPM_1998_4_2_a8
Let $\mathcal{O}(U)$ be the Fréchet algebra of holomorphic functions on a domain $U\subset\mathbb{C}$, endowed with the compact-open topology. In this paper we study certain properties ensuring the freedom of finitely generated Fréchet $\mathcal{O}(U)$-modules. In particular, it is proved that each flat finitely generated Fréchet $\mathcal{O}(U)$-module is free.
