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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Homomorphisms of rings of germs of analytic functions


Author: William R. Zame
Journal: Proc. Amer. Math. Soc. 33 (1972), 410-414
MSC: Primary 32.50
MathSciNet review: 0289808
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Abstract: Let S and S' be complex analytic manifolds with S Stein. Let $ X \subset S$ and $ X' \subset S'$ be compact sets with X holomorphically convex. Denote by $ \mathcal{O}(X)$ (respectively $ \mathcal{O}(X')$) the ring of germs on X (respectively X') of functions analytic near X (respectively X'). It is shown that each nonzero homomorphism of $ \mathcal{O}(X)$ into $ \mathcal{O}(X')$ is given by composition with an analytic map defined in a neighborhood of X' and taking values in S.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0289808-6
Keywords: Germs of analytic functions, holomorphically convex sets
Article copyright: © Copyright 1972 American Mathematical Society