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Proceedings of the American Mathematical Society

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



Continuity of systems of derivations on $ F$-algebras

Author: R. L. Carpenter
Journal: Proc. Amer. Math. Soc. 30 (1971), 141-146
MSC: Primary 46.55; Secondary 32.00
MathSciNet review: 0283574
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Abstract: Let A be a commutative semisimple F-algebra with identity, and let $ {D_0},{D_1}, \cdots $ be a system of derivations from A into the algebra of all continuous functions on the spectrum of A. It is shown that the transformations $ {D_0},{D_1}, \cdots $ are necessarily continuous. This result is used to obtain a characterization of derivations on $ {\text{Hol}}(\Omega )$ where $ \Omega $ is an open polynomially convex subset of $ {C^n}$.

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Keywords: F-algebra, derivation, systems of derivations, continuity of derivations
Article copyright: © Copyright 1971 American Mathematical Society

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