A note on topological divisors of zero and division algebras

We prove that normed unital complex (possibly non-associative) algebras with no non-zero left topological divisor of zero are isomorphic to the field C of complex numbers. We also show the existence of a complete normed unital infinite-dimensional complex algebra with no non-zero two-sided topologic...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2015-03, Vol.109 (1), p.93-100
Main Authors: Marcos, J. Carlos, Rodríguez-Palacios, Ángel, Velasco, M. Victoria
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Complex numbers
Division
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Texts
Theoretical
Topology
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Summary:We prove that normed unital complex (possibly non-associative) algebras with no non-zero left topological divisor of zero are isomorphic to the field C of complex numbers. We also show the existence of a complete normed unital infinite-dimensional complex algebra with no non-zero two-sided topological divisor of zero.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-014-0168-4