A new simple proof of the Gel′fand-Mazur-Kaplansky theorem

Cabrera García, Miguel; Rodríguez-Palacios, Ángel

doi:10.1090/S0002-9939-1995-1231298-6

A new simple proof of the Gel′fand-Mazur-Kaplansky theorem
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by Miguel Cabrera García and Ángel Rodríguez-Palacios PDF

Proc. Amer. Math. Soc. 123 (1995), 2663-2666 Request permission

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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