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
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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},
     year = {1998},
     volume = {4},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_2_a8/}
}
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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/