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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new simple proof of the Gelfand-Mazur-Kaplansky theorem


Authors: Miguel Cabrera García and Ángel Rodríguez-Palacios
Journal: Proc. Amer. Math. Soc. 123 (1995), 2663-2666
MSC: Primary 46H20
MathSciNet review: 1231298
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Abstract: We provide an almost purely algebraic proof of Kaplansky's refinement of the Gelfand-Mazur theorem asserting that the reals, complex, and quaternions are the only associative normed real algebras with no nonzero topological divisors of zero.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1231298-6
PII: S 0002-9939(1995)1231298-6
Article copyright: © Copyright 1995 American Mathematical Society