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Proceedings of the American Mathematical Society

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

 

 

Uniqueness of topology for commutative semisimple $ F$-algebras


Author: R. L. Carpenter
Journal: Proc. Amer. Math. Soc. 29 (1971), 113-117
MSC: Primary 46J05
DOI: https://doi.org/10.1090/S0002-9939-1971-0298424-0
MathSciNet review: 0298424
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Abstract: Let B be an F-algebra and A be a commutative semisimple F-algebra such that the spectrum of A contains no isolated points. We prove that any homomorphism of B onto A is necessarily continuous. Let A be a commutative semisimple algebra. We prove that there is at most one topology with respect to which A is an F-algebra.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0298424-0
Keywords: F-algebra, commutative, semisimple, uniqueness of topology, continuity of homomorphisms
Article copyright: © Copyright 1971 American Mathematical Society