The ring of holomorphic functions on a Stein compact set as a unique factorization domain

Dales, H.G. (1974) The ring of holomorphic functions on a Stein compact set as a unique factorization domain. Proceedings of the American Mathematical Society, 44 (1). pp. 88-92. ISSN 0002-9939

Abstract

Let $ \Gamma $ be the ring of germs of analytic functions on a Stein compact subset $ K$ of a complex-analytic space. Necessary and sufficient conditions on $ K$ for $ \Gamma $ to be a unique factorization domain are given.