Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@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},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1998},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a8/
%G ru
%F FPM_1998_4_2_a8
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/