Cohomology, maximal ideals, and point evaluations
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- by Alexander Nagel PDF
- Proc. Amer. Math. Soc. 42 (1974), 47-50 Request permission
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.References
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
Additional Information
- © Copyright 1974 American Mathematical Society
- 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