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 Fr\'echet 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 Fr\'echet $\mathcal{O}(U)$-modules. In particular, it is proved that each flat finitely generated Fr\'echet $\mathcal{O}(U)$-module is free.

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