Jordan homomorphisms of the symmetric elements of a ring with involution (Q2529224)

This paper generalizes the theorem of \textit{N. Jacobson} and \textit{C. E. Rickart} [Trans. Am. Math. Soc. 72, 310--322 (1952; Zbl 0046.25603)] with regards to the extending of Jordan homomorphisms of \(S\), the set of symmetric elements of a ring \(R\), with identity, into \(R'\) to an associative homomorphism of \(R\) into \(R'\) by giving a number of weaker hypotheses on the ring. These hypotheses in general are concerned with the existence of a number of symmetric idempotents, and with the mixing of subrings in the Pierce decomposition. The author also considers the related questions for Jordan derivations of \(S\).