Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.55, 32.00

Retrieve articles in all journals with MSC: 46.55, 32.00


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0283574-5
PII: S 0002-9939(1971)0283574-5
Keywords: F-algebra, derivation, systems of derivations, continuity of derivations
Article copyright: © Copyright 1971 American Mathematical Society