Ring isomorphisms of Jordan-Banach algebras (Q2785920)

Let \(A\) and \(B\) be noncommutative semisimple complex Jordan-Banach algebras. The main result in this paper asserts that if \(f:A\longrightarrow B\) is a ring isomorphism then \(A = A_1 \oplus A_2 \oplus A_3 \) where \(A_1,\) \(A_2,\) \(A_3 \) are closed two-sided ideals of \(A\) such that: i) \(A_1 \) is finite-dimensional; ii) the restriction of \(f\) to \(A_2 \) (resp. \(A_3 \) ) is linear (resp. antilinear ). This theorem is a noncommutative Jordan version of a well-known result by \textit{I. Kaplansky} [Can. J. Math. 6, 374-381 (1954; Zbl 0058.10505)]. The proof uses Kaplansky's methods and it depends heavily of the structure theory of noncommutative Jordan-Banach algebras with finite spectrum given by \textit{M. Benslimane} and \textit{A. Kaidi} [J. Algebra 113, 201-206 (1988; Zbl 0692.46044)].NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].