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Proceedings of the American Mathematical Society

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

 

 

Cohomology, maximal ideals, and point evaluations


Author: Alexander Nagel
Journal: Proc. Amer. Math. Soc. 42 (1974), 47-50
MSC: Primary 32E25; Secondary 46J10
DOI: https://doi.org/10.1090/S0002-9939-1974-0328122-9
MathSciNet review: 0328122
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Abstract: We consider algebras A of continuous complex valued functions, which are given as the set of global sections of a sheaf $ \mathcal{S}$ on a topological space X. Under the hypothesis that all the higher cohomology groups of the sheaf are zero, we investigate the relationship between ideals in A, kernels of algebra homomorphisms of A into the complex numbers C, and sets of functions vanishing at a point of X. As applications, we obtain some simple proofs of theorems about ideals in certain algebras of holomorphic functions.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328122-9
Keywords: Cohomology, maximal ideals, point evaluation, Koszul complex, analytic functions, domain of holomorphy, Stein space
Article copyright: © Copyright 1974 American Mathematical Society