Derivations with invertible values in rings with involution (Q1072625)

The authors extend the result of \textit{J. Bergen, I. N. Herstein} and \textit{C. Lanski} [Can. J. Math. 35, 300-310 (1983; Zbl 0522.16031)] which characterizes rings having a derivation whose nonzero values are invertible, to the case of involutions. Specifically let R be a 2-torsion free semi-prime ring with involution and derivation d satisfying d(s) is zero or invertible for each symmetric element s. The authors prove that R must be either a division ring D, \(M_ 2(D)\), the direct sum of either of these with its opposite ring, or \(M_ 4(F)\) with symplectic involution. The proof is computational and makes clever use of the Jacobson density theorem.