FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1998, VOLUME 4, NUMBER 2, PAGES 585-594

On the conditions ensuring the freedom of topological modules over algebras of holomorphic functions

A. Yu. Pirkovskii

Abstract

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Let $ \mathcal {O}(U) $ be the Fréchet algebra of holomorphic functions on a domain U ⊂ 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.


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