Topological \(J\)-divisors of zero in unitary \(p\)-normed Jordan algebras
For associative normed real algebras it is well-known [cf. \textit{I. Kaplansky}, Duke Math. J. 16, 399-418 (1949; Zbl 0033.18701)] that they are isomorphic to the real field, the complex field or the quaternions, if and only if they do not have non-trivial topological divisors of zero. This result was extended in the Jordan case by \textit{A. M. Kaïdi} [Ann. Sci. Univ. Blaise Pascal, Clermont II, Sér. Math. 27, 119-124 (1991; Zbl 0794.17001)]. In this paper the authors generalize these results in the case of \(p\)-normed Jordan algebras without non-trivial Jordan topological divisors of zero. In the complex case they prove that they are isomorphic to the complex field. In the real case they prove that they are quadratic division algebras (which may be of infinite dimension).
scientific article; zbMATH DE number 1336363